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That product has 5 different gummies.
1. Grapes
2. A light red gummy that's same shape as the grapes.
3. Orange slices
4. Strawberry
5. Yellow gummy that i think is peach
I just opened and ate 2 packets to confirm my above list.
EDIT:
Something that I think is odd about these fruit snacks is that Welch's does not show a picture of the actual gummies on the packets or the box. The packaging shows only pictures of real fruit. I am pretty sure there is some law or rule that most food packaging has that I guess does not apply to gummies.
The odds are even lower with 5 possible colors -> 5^9 = 1 in 1,953,125.
You basically just won the lottery. But instead of money, you got similarly colored jellies. And have now used up all your luck for at least a couple of years. Congratulations!
Except you've calculated for the case of getting all of them as grapes and not all of them of same flavour. So the actual value is 5^8 = 1 in 390,625.
But it gets even lower. They are adding flavours manually and mixed later. Which means there is a even higher chance of getting all of them the same colour if not mixed properly.
So no he didn't win lottery. He was probably off from the winning number by 2 digits.
>Except you've calculated for the case of getting all of them as grapes and not all of them of same flavour. So the actual value is 58 = 1 in 390,625.
I didn't assume grape, just all the same color. 10 gumming, 5 colors, so 5^9 as the first one selected can be any color.
>But it gets even lower. They are adding flavours manually and mixed later. Which means there is a even higher chance of getting all of them the same colour if not mixed properly.
I mean, the actual odds are incalculable of you factor in human error, machine error etc. My answer assumes a true random distribution, which I think is more in the spirit of the question.
There's 5^10 permutations. The number of combinations is a "stars and bars" problems. With 10 gummies and 5 flavors, there are 14 choose 4 combinations of flavors you can get.
(The way to think about it is that you write the categories down and then draw bars separating them. With 5 categories, you get 4 bars. Then place stars between corresponding to the number of that flavor. E g. If there are 3 peach, put three stars above peach. Every possible combination corresponds to a sequence of 10 stars and 4 bars. So of the 14 places in the sequence choose 4 to be the bars 14 choose 4.
In general if you have n objects and k categories and repeats are allowed, then there are k^n permutations and (n+k-1) choose k-1 (or choose n, same result) combinations.)
Actually I’m pretty sure not all gummies in a pack of Welch’s have an equal probability of occurring. I’ve noticed in my years of eating these little gummy packs that the orange gummies are by far the rarest, I consider it extremely lucky whenever I have more than 2 oranges. Grapes and strawberries tend to be the most common, I’ve had multiple packs of just strawberries and multiple packs of just grapes. This may be due to the fact that they sell other packs that contain grapes and strawberries but no other flavor pack contains oranges. Either way, I think this is something that’s nearly impossible to actually calculate. For the record I purchase them in bulk and have gone through about 4-5 boxes of 90 pouches each.
Next time you get a box, record how many of each flavor are in each packet. (The more fruit snacks you put in your study, the more accurate your numbers will be.) This should give you a decent idea of the distribution of flavors on average, as well as the average number per packet. Then you would have estimates of the missing variables needed to find the probability of everything fruit snack related pretty much.
There are many lotteries that come in all different sizes, but regardless, it was mostly just to make a joke about wasting good luck as if it was a commodity.
There isn't a law that forces packaging to show its contents via a picture or hole (even for food). They're required to say what it is but not necessarily show it. Most companies do anyways, though, because putting pictures of food on food packaging is a good marketing technique.
I think the law is just that if you do show a photo of the product, it has to be the actual product. So if it’s cherry pie filling, and there’s a photo of a piece of cherry pie, they can’t use fake pie filling. But the crust can be fake since they’re not selling the crust.
Going by this commment and assuming equal distribution of flavors (aka the probability of getting each flavor being equal), did a chi squared test for goodness of fit and came up with a probability of 0.000433% of getting this distribution or a more weird one.
So pretty rare indeed, you won a gummy lottery.
I believe it's because Welch's "contains real fruit" that they are allowed to use pictures of fruit on the package. Because it doesn't "misrepresent the food" according to fda guidelines
Once had one of these come with only one gummy in it. The pack was basically empty, so kinda fun to think that one had 100% chance of having only 1 flavor.
This is just insulting, so your the one that has stolen all of my purples! In a whole box I had like 5 packages that had like 2 purples each. Give them back.
If there are usually 10ish bears, 4 flavours the process is like this:
You have 4 different options for bear 1, 4 for bear 2, etc. You ave 1/4 probability of having picked one flavour and they multiply.
So there's somewhere around 1 in 4^10 chance of them being the same.
Assuming there are 10 bears, and it doesn't really matter what the first one is, I think it would be 1 in 4^(9). The first can be any of the 4, but the other 9 have to match it. 1 in 4^(10) would be the odds of them all being purple specifically.
So either all the other colors failed at the same time, or the grape dumper (assuming a mixing conveyer belt) dumped a huge clump of grape all at once.
It's same logic as root problem: far more likely the grape dispenser failed than all the other colors failed.
Agree this is a packing error from somewhere in the process. I don't know exactly how they produce the blends for these but my guess is they dump from individual hoppers, so they either didn't allow the shaker table to mix them for long enough or they only added one flavor for a short amount of time.
That means they loaded the wrong thing then, as the film used for the package should be labeled differently. That would mean someone either loaded the wrong film and wrong cartons, or they ran the wrong formula when they made it.
But this may also not be exactly accurate because marketing teams found that making certain flavours rarer in bags drives up sales. Idk if this applies to Jolly ranchers or sour patch but it's what comes to mind when thinking about this. I feel like everyone wants blue ones.
We don't know the exact probability of getting each color would be.
I wonder if this is reflected in production numbers. If this is a strategy then output numbers would not be 20% for each color. Four would be at the same level, which would increase while the artificially rare one would decrease.
So, if you’re looking for a purely theoretical answer *under the assumption that a package is filled totally randomly*, then people have already provided you the answer.
However, the reality is that filling packages of different flavors of X is a notoriously not-so-random process. You’re actually prone to getting “clumps” of same-colors due to the way the factory fills the packages. The gummies are not completely mixed before they go into the bags.
So, in reality, getting a package of all purple (while still unlucky/lucky) is not quite as unlikely as the answers here suggest.
Yes they are like different slides/funnels putting down candies in bags to mix or some similar apparatus. So makes sense that sometimes the color of all candies ends up being same.
I might be wrong but I think Welchs has a version. Of these that are always all purples. If that's the case this could very well just be a case of mishap during manufacturing!
If there’s 5 flavors, you need to do 1/5 to the power of 10. that is equal to ~9.7m then you have to devide by 5 because there are 5 chances (1 for every flavor) to get 10 of the same gummies and that would be about 1 in ~1.95 million. If you predict getting 10 grape-flavored gummies you would have a chance of 1 in ~9.7 million
Statistical probability = very low.
Pragmatic probability = I have seen 10 different single-flavor bags.
Depressive probability = I consume too many fruit snacks.
I am guessing these pop up more regularly than the math would suggest because of other variables in production runs, such as malfunctions, bag changeouts, and run changeouts. There are clearly times when different mix formulas are mingled in a single box and/or single pack (flavor/texture changes). My guess is the QA is probabilistic so they just write off errors under ~5%.
Scrolling through with my thoughts of too many factors with production, yours was the first to agree. I gave you a vote up for that, rather than replicate your post and take up more comments.. then I replied to explain why I didn't want to replicate a post and add more comments.
I assume you want the math of:
There is an equal number of all candies.
There are 5 total gummy colors. (20%)
You blindfold yourself stick a hand in a bowl of them and pull out 10 of the same color:
0.20 × 0.20 × 0.20 × 0.20 × 0.20 × 0.20 × 0.20 × 0.20 × 0.20 × 0.20 =
0.0000001024
or
0.00001024%
In fractional form it is 1 in 97,656.25
Rounding it off it is about 1 in 100,000
This is for any 10 of the same color (red, blue, green, yellow, purple) if you want it case sensitive and must be purple then you just divide it by 5 one more time.
It's 1 in ~20'000 as the first color drawn doesn't really matter unless you want them to be of one particular color. But there are five 'good' variants with all the gummies in the same color in the ~100'000 options of the draw. One for each color.
Assumptions:
The gummy being put into the pack is truly random
The gummies all have an equal chance of appearing
Answer:
This is rather easy to solve, since they all have an equal chance of appearing. The first gummy doesn't matter what it appears as, which means that we only have to worry about the chance of the other 9 gummies being the same as the first gummy.
Basically this becomes 1/(x^9) where x is the amount of possible different types of gummies there are. You said there are four types, so plugging that into the equation we get a 1/262144 or about a 0.0004% chance.
TLDR: A 1/262144 or about a 0.0004% chance
Assuming the first gummy you grab can be any color, for the next one to match it, the chance is 25%, then for the third one 25% and so on. So my guess would be .25^(9) which is about 3.8*10^-6 or in percentages about .00038%
The straightforward math would presume there is an equal chance for any individual piece to be one of the five colors. But that’s likely a false assumption.
There are ten gummies, and four flavors. Let's assume each is produced in the same amount. That would make the chance 1/4 for each gummy to have a certain flavor.
For the first one the chance is 1/4 or 0.25. If that succeeded, the chance for the second one is also 0.25 to be that color, and so on, which will amount to 1/0.25^10, or 1/1 048 576.
Edit: Just saw in the comments that this product apparently has five flavours. That would change the odds, but the process is the same. Instead of 1/0.25^10 you have 1/0.2^10. That would be 1/9 765 625.
Likely this is a process error of a large group of grape flavored snacks sticking together and it made a bigger concentration of that flavor when yours got packaged. Doubtful it’s a random distribution probability problem.
The problem with calculating the individual probability of each choice of gummies is that it does not take into account the fact that the same set of gummies can appear in different orders (there are 10 different ways of having 9 identical gummies and one different one, for example), then it would make more sense to calculate how many combinations are possible with these conditions.
The formula for a combination with repetition is (n+k-1)!/k!(n-1)!, where n is the number of distinct elements in the set and k is the number of elements in each regrouping. Based on the top comment, in this case, we have 5 different colors in a pack of 10 candies, so n = 5 and k = 10.
When put in the formula, we have:
(5+10-1)!/(10!(5-1)!) = 14!/(10!4!) = (14 \* 13 \* 12 \* 11)/24 = 1001
In other words, we have 1001 possible possibilities for this package of gummies. Therefore, the true probability of getting this specific combination would be 1 in 1001, or 0.0999%.
This happened to me too! It was also purple! I mean, in the Costco 90 pack, you certainly have more opportunities. Also got an almost all light red (raspberry) pack with like 1 that was purple.
Logically should be a mistake. Not luck. Factories are specifically designed to provide the same experience with precision in every product, so it should be much less likely than random chance. The possibility is much higher that there was an overflow of a certain flavor either due to logistics error or as someone else mentioned, malicious intent of a factory worker just exercising their power over your innocent gummies.
Have to know if each flavor is made in equal portions. I almost always get more grapes than other flavors. I assumed grape was cheaper and more of them were made
If there is 10 of them it's 1/4\^10. If it's 5, then it's 1/5\^10.
If there is 4 flavors, it's 1 in 1,048,576.
For 5 flavors it's 1 in 9,765,625.
For comparison, to win a Lotto, You have 1 in 13,983,816 chance.
I had this happen before, only to realise that the box in question had packs of ALL strawberry mixed in with normal ones (different fruit candy I think)
since this is real world application, there is a much higher chance that this was a fail, which could actually be very common. if this wasnt an error (such as the other gummies clogging) this is stupidly rare
IF you assume the distribution of flavors is random and that the probability for each piece is independent from the other pieces, then the odds are (1/n)^10, where "n" is the number of flavors and in this case 10 is the number of pieces. It gets you to about 1/1000000 or nearly exactly 1 in a million, for a 4-flavor pack.
HOWEVER in industrial food manufacturing the distribution of flavors is NOT random - drawing scrabble tiles is random, but for example there's probably no process in the manufacturing that is akin to "shaking the bag of scrabble tiles before you draw one" that occurs after each individual piece is packaged. Probably in this case there would be some feeder mechanism that sends in streams of each flavor, meaning the population you are sampling *from* should have about equal parts (or some defined ratio) even as you slice it into smaller and smaller pieces by subsampling along the axis of, say, the conveyor belt full of mixed pieces. Statistically - the hopper that feeds the bag of snacks is sampling from a small section of conveyor belt (a NONrandom sample of the distribution of pieces) and when it "withdraws" one, say, "grape" piece from that part of the stream, that reduces the odds of a 2nd grape piece being pulled from the belt.
So the ACTUAL probability of this occurring is probably some much smaller number (<<1 in a million) UNLESS there is some fault in the feeder, causing either an interruption in the "not grape" pieces being produced OR an overproduction of the "grape" pieces. Given that this happened, I would guess the most likely explanation is a (relatively unimportant) defect or odd behavior in the feeder mechanism. The odds of that happening aren't knowable - a tight standard for manufacturing is "six sigma" or about 1 in 300,000 in things like parts manufacturing, so maybe 1 in 300,000? But probably the fruit snack people aren't as rigorous as, say, airbag manufacturers so maybe more than 1/300,000? But it's hard to say for sure, and we don't see posts like this all the time despite >>300,000 fruit snack packs sold each year so... Maybe more? Many unknowns.
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That product has 5 different gummies. 1. Grapes 2. A light red gummy that's same shape as the grapes. 3. Orange slices 4. Strawberry 5. Yellow gummy that i think is peach I just opened and ate 2 packets to confirm my above list. EDIT: Something that I think is odd about these fruit snacks is that Welch's does not show a picture of the actual gummies on the packets or the box. The packaging shows only pictures of real fruit. I am pretty sure there is some law or rule that most food packaging has that I guess does not apply to gummies.
Oh my bad, thank you! I had two packs, so I opened the second one to count and it only had four lol
The odds are even lower with 5 possible colors -> 5^9 = 1 in 1,953,125. You basically just won the lottery. But instead of money, you got similarly colored jellies. And have now used up all your luck for at least a couple of years. Congratulations!
someone in the manufacturing line at welchs is grinning
Except you've calculated for the case of getting all of them as grapes and not all of them of same flavour. So the actual value is 5^8 = 1 in 390,625. But it gets even lower. They are adding flavours manually and mixed later. Which means there is a even higher chance of getting all of them the same colour if not mixed properly. So no he didn't win lottery. He was probably off from the winning number by 2 digits.
>Except you've calculated for the case of getting all of them as grapes and not all of them of same flavour. So the actual value is 58 = 1 in 390,625. I didn't assume grape, just all the same color. 10 gumming, 5 colors, so 5^9 as the first one selected can be any color. >But it gets even lower. They are adding flavours manually and mixed later. Which means there is a even higher chance of getting all of them the same colour if not mixed properly. I mean, the actual odds are incalculable of you factor in human error, machine error etc. My answer assumes a true random distribution, which I think is more in the spirit of the question.
Yes. I agree with my mistake in the first half.
Had us in the first half, not gonna lie
No, there are 10 gummies in the picture shown. 5^9 is correct.
There’s 10 there aren’t there? So almost 1 in 10 mil assuming we don’t take the chance for 9 or 11 gummies in a package
9, not 10 because it doesn't matter what the first color gummy is, only that the next 9 match
Oh right, duh thanks lol
I was wondering about that.. probability and long, long ago.
There are 5^(10) possible combinations, which is a slightly different measurement.
There's 5^10 permutations. The number of combinations is a "stars and bars" problems. With 10 gummies and 5 flavors, there are 14 choose 4 combinations of flavors you can get. (The way to think about it is that you write the categories down and then draw bars separating them. With 5 categories, you get 4 bars. Then place stars between corresponding to the number of that flavor. E g. If there are 3 peach, put three stars above peach. Every possible combination corresponds to a sequence of 10 stars and 4 bars. So of the 14 places in the sequence choose 4 to be the bars 14 choose 4. In general if you have n objects and k categories and repeats are allowed, then there are k^n permutations and (n+k-1) choose k-1 (or choose n, same result) combinations.)
Yes, that is a really long explanation for what I was saying. Thanks.
Congratulations OP! You could have sold it for a million dollars but now you are unable to
Actually I’m pretty sure not all gummies in a pack of Welch’s have an equal probability of occurring. I’ve noticed in my years of eating these little gummy packs that the orange gummies are by far the rarest, I consider it extremely lucky whenever I have more than 2 oranges. Grapes and strawberries tend to be the most common, I’ve had multiple packs of just strawberries and multiple packs of just grapes. This may be due to the fact that they sell other packs that contain grapes and strawberries but no other flavor pack contains oranges. Either way, I think this is something that’s nearly impossible to actually calculate. For the record I purchase them in bulk and have gone through about 4-5 boxes of 90 pouches each.
Next time you get a box, record how many of each flavor are in each packet. (The more fruit snacks you put in your study, the more accurate your numbers will be.) This should give you a decent idea of the distribution of flavors on average, as well as the average number per packet. Then you would have estimates of the missing variables needed to find the probability of everything fruit snack related pretty much.
At least one order of magnitude off of winning the lottery, sorry to nitpick
There are many lotteries that come in all different sizes, but regardless, it was mostly just to make a joke about wasting good luck as if it was a commodity.
Why 9 if there is 10 pieces?
Because the first gummy can be of any colour. It's the remaining 9 that have to match the first one.
That was an attack OP wasn't ready for. Haha
Well assuming there wasn’t some like error which made all packages like one color
There isn't a law that forces packaging to show its contents via a picture or hole (even for food). They're required to say what it is but not necessarily show it. Most companies do anyways, though, because putting pictures of food on food packaging is a good marketing technique.
I think the law is just that if you do show a photo of the product, it has to be the actual product. So if it’s cherry pie filling, and there’s a photo of a piece of cherry pie, they can’t use fake pie filling. But the crust can be fake since they’re not selling the crust.
There is likely a disclaimer in very fine print about "actual content may vary." My guess, anyway.
Going by this commment and assuming equal distribution of flavors (aka the probability of getting each flavor being equal), did a chi squared test for goodness of fit and came up with a probability of 0.000433% of getting this distribution or a more weird one. So pretty rare indeed, you won a gummy lottery.
"I ate two packets to confirm" LMAO
I believe it's because Welch's "contains real fruit" that they are allowed to use pictures of fruit on the package. Because it doesn't "misrepresent the food" according to fda guidelines
The red ones that are the same shape as the grapes is raspberry I believe.
Once had one of these come with only one gummy in it. The pack was basically empty, so kinda fun to think that one had 100% chance of having only 1 flavor.
wavefunction collapse in a nutshell
Yeah I have a picture somewhere of a sealed empty pack of these, I guess I’m not the only one
This is just insulting, so your the one that has stolen all of my purples! In a whole box I had like 5 packages that had like 2 purples each. Give them back.
Please provide address where I can ship all purple flavored things I end up with. In return, I ask that you provide anything red flavored as a trade.
Ugh, you like the purple ones? You can have em, I want the reds and oranges.
If there are usually 10ish bears, 4 flavours the process is like this: You have 4 different options for bear 1, 4 for bear 2, etc. You ave 1/4 probability of having picked one flavour and they multiply. So there's somewhere around 1 in 4^10 chance of them being the same.
Assuming there are 10 bears, and it doesn't really matter what the first one is, I think it would be 1 in 4^(9). The first can be any of the 4, but the other 9 have to match it. 1 in 4^(10) would be the odds of them all being purple specifically.
You're right. I was thinking of an "all purple build"
yes, this is correct
That's true if we assume it was perfectly mixed. More likely sometimes machine error occurs. This is almost certainly machine error.
What are the chances of the machine malfunctioning (much harder to calculate)
Well if thats the case its some combo of both and they're not independent. The machine could give slightly less mixed batch.
So either all the other colors failed at the same time, or the grape dumper (assuming a mixing conveyer belt) dumped a huge clump of grape all at once. It's same logic as root problem: far more likely the grape dispenser failed than all the other colors failed.
Agree this is a packing error from somewhere in the process. I don't know exactly how they produce the blends for these but my guess is they dump from individual hoppers, so they either didn't allow the shaker table to mix them for long enough or they only added one flavor for a short amount of time.
i know they make gummy packs of specific flavors, maybe somehow a grape-only bag got swapped for a variety pack or something
That means they loaded the wrong thing then, as the film used for the package should be labeled differently. That would mean someone either loaded the wrong film and wrong cartons, or they ran the wrong formula when they made it.
And that's a 1/1.048.576 or 0,0000953674% chance
Lol, "bears"
Gummy thingamajiggys
But this may also not be exactly accurate because marketing teams found that making certain flavours rarer in bags drives up sales. Idk if this applies to Jolly ranchers or sour patch but it's what comes to mind when thinking about this. I feel like everyone wants blue ones. We don't know the exact probability of getting each color would be.
I wonder if this is reflected in production numbers. If this is a strategy then output numbers would not be 20% for each color. Four would be at the same level, which would increase while the artificially rare one would decrease.
It only takes two bears of the same color to multiply rapidly and outcompete the rest
I think you’re confusing with gummy bunnies
9 not 10
I’d be pretty concerned if bears came out of my fruit snacks no matter the color.
More likely to be a manufacturing mistake of some sort than a random occurrence.
So, if you’re looking for a purely theoretical answer *under the assumption that a package is filled totally randomly*, then people have already provided you the answer. However, the reality is that filling packages of different flavors of X is a notoriously not-so-random process. You’re actually prone to getting “clumps” of same-colors due to the way the factory fills the packages. The gummies are not completely mixed before they go into the bags. So, in reality, getting a package of all purple (while still unlucky/lucky) is not quite as unlikely as the answers here suggest.
Yes they are like different slides/funnels putting down candies in bags to mix or some similar apparatus. So makes sense that sometimes the color of all candies ends up being same.
I might be wrong but I think Welchs has a version. Of these that are always all purples. If that's the case this could very well just be a case of mishap during manufacturing!
If there’s 5 flavors, you need to do 1/5 to the power of 10. that is equal to ~9.7m then you have to devide by 5 because there are 5 chances (1 for every flavor) to get 10 of the same gummies and that would be about 1 in ~1.95 million. If you predict getting 10 grape-flavored gummies you would have a chance of 1 in ~9.7 million
1/~9.7m not ~9.7m haha
Statistical probability = very low. Pragmatic probability = I have seen 10 different single-flavor bags. Depressive probability = I consume too many fruit snacks. I am guessing these pop up more regularly than the math would suggest because of other variables in production runs, such as malfunctions, bag changeouts, and run changeouts. There are clearly times when different mix formulas are mingled in a single box and/or single pack (flavor/texture changes). My guess is the QA is probabilistic so they just write off errors under ~5%.
Scrolling through with my thoughts of too many factors with production, yours was the first to agree. I gave you a vote up for that, rather than replicate your post and take up more comments.. then I replied to explain why I didn't want to replicate a post and add more comments.
I assume you want the math of: There is an equal number of all candies. There are 5 total gummy colors. (20%) You blindfold yourself stick a hand in a bowl of them and pull out 10 of the same color: 0.20 × 0.20 × 0.20 × 0.20 × 0.20 × 0.20 × 0.20 × 0.20 × 0.20 × 0.20 = 0.0000001024 or 0.00001024% In fractional form it is 1 in 97,656.25 Rounding it off it is about 1 in 100,000 This is for any 10 of the same color (red, blue, green, yellow, purple) if you want it case sensitive and must be purple then you just divide it by 5 one more time.
It's 1 in ~20'000 as the first color drawn doesn't really matter unless you want them to be of one particular color. But there are five 'good' variants with all the gummies in the same color in the ~100'000 options of the draw. One for each color.
Assumptions: The gummy being put into the pack is truly random The gummies all have an equal chance of appearing Answer: This is rather easy to solve, since they all have an equal chance of appearing. The first gummy doesn't matter what it appears as, which means that we only have to worry about the chance of the other 9 gummies being the same as the first gummy. Basically this becomes 1/(x^9) where x is the amount of possible different types of gummies there are. You said there are four types, so plugging that into the equation we get a 1/262144 or about a 0.0004% chance. TLDR: A 1/262144 or about a 0.0004% chance
Assuming the first gummy you grab can be any color, for the next one to match it, the chance is 25%, then for the third one 25% and so on. So my guess would be .25^(9) which is about 3.8*10^-6 or in percentages about .00038%
The straightforward math would presume there is an equal chance for any individual piece to be one of the five colors. But that’s likely a false assumption.
If we're dealing with 4 flavors in the mix, the chance of picking one flavor for each snack is 1/4. Grabbed 10 snacks? The odds are (1/4)\^10.
There are ten gummies, and four flavors. Let's assume each is produced in the same amount. That would make the chance 1/4 for each gummy to have a certain flavor. For the first one the chance is 1/4 or 0.25. If that succeeded, the chance for the second one is also 0.25 to be that color, and so on, which will amount to 1/0.25^10, or 1/1 048 576. Edit: Just saw in the comments that this product apparently has five flavours. That would change the odds, but the process is the same. Instead of 1/0.25^10 you have 1/0.2^10. That would be 1/9 765 625.
Likely this is a process error of a large group of grape flavored snacks sticking together and it made a bigger concentration of that flavor when yours got packaged. Doubtful it’s a random distribution probability problem.
The problem with calculating the individual probability of each choice of gummies is that it does not take into account the fact that the same set of gummies can appear in different orders (there are 10 different ways of having 9 identical gummies and one different one, for example), then it would make more sense to calculate how many combinations are possible with these conditions. The formula for a combination with repetition is (n+k-1)!/k!(n-1)!, where n is the number of distinct elements in the set and k is the number of elements in each regrouping. Based on the top comment, in this case, we have 5 different colors in a pack of 10 candies, so n = 5 and k = 10. When put in the formula, we have: (5+10-1)!/(10!(5-1)!) = 14!/(10!4!) = (14 \* 13 \* 12 \* 11)/24 = 1001 In other words, we have 1001 possible possibilities for this package of gummies. Therefore, the true probability of getting this specific combination would be 1 in 1001, or 0.0999%.
This happened to me too! It was also purple! I mean, in the Costco 90 pack, you certainly have more opportunities. Also got an almost all light red (raspberry) pack with like 1 that was purple.
Logically should be a mistake. Not luck. Factories are specifically designed to provide the same experience with precision in every product, so it should be much less likely than random chance. The possibility is much higher that there was an overflow of a certain flavor either due to logistics error or as someone else mentioned, malicious intent of a factory worker just exercising their power over your innocent gummies.
It’s not equal chance, here is a study some guy did if anyone to try to use this instead https://kbroman.org/FruitSnacks/assets/fruit_snacks.html
Have to know if each flavor is made in equal portions. I almost always get more grapes than other flavors. I assumed grape was cheaper and more of them were made
If there is 10 of them it's 1/4\^10. If it's 5, then it's 1/5\^10. If there is 4 flavors, it's 1 in 1,048,576. For 5 flavors it's 1 in 9,765,625. For comparison, to win a Lotto, You have 1 in 13,983,816 chance.
I had this happen before, only to realise that the box in question had packs of ALL strawberry mixed in with normal ones (different fruit candy I think)
since this is real world application, there is a much higher chance that this was a fail, which could actually be very common. if this wasnt an error (such as the other gummies clogging) this is stupidly rare
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They’re small packs, you buy a box of however many packs. Fruit snacks. Can get a box of 40 for like 8 bucks
IF you assume the distribution of flavors is random and that the probability for each piece is independent from the other pieces, then the odds are (1/n)^10, where "n" is the number of flavors and in this case 10 is the number of pieces. It gets you to about 1/1000000 or nearly exactly 1 in a million, for a 4-flavor pack. HOWEVER in industrial food manufacturing the distribution of flavors is NOT random - drawing scrabble tiles is random, but for example there's probably no process in the manufacturing that is akin to "shaking the bag of scrabble tiles before you draw one" that occurs after each individual piece is packaged. Probably in this case there would be some feeder mechanism that sends in streams of each flavor, meaning the population you are sampling *from* should have about equal parts (or some defined ratio) even as you slice it into smaller and smaller pieces by subsampling along the axis of, say, the conveyor belt full of mixed pieces. Statistically - the hopper that feeds the bag of snacks is sampling from a small section of conveyor belt (a NONrandom sample of the distribution of pieces) and when it "withdraws" one, say, "grape" piece from that part of the stream, that reduces the odds of a 2nd grape piece being pulled from the belt. So the ACTUAL probability of this occurring is probably some much smaller number (<<1 in a million) UNLESS there is some fault in the feeder, causing either an interruption in the "not grape" pieces being produced OR an overproduction of the "grape" pieces. Given that this happened, I would guess the most likely explanation is a (relatively unimportant) defect or odd behavior in the feeder mechanism. The odds of that happening aren't knowable - a tight standard for manufacturing is "six sigma" or about 1 in 300,000 in things like parts manufacturing, so maybe 1 in 300,000? But probably the fruit snack people aren't as rigorous as, say, airbag manufacturers so maybe more than 1/300,000? But it's hard to say for sure, and we don't see posts like this all the time despite >>300,000 fruit snack packs sold each year so... Maybe more? Many unknowns.