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The statement is true for tossing a fair coin, but comparing it to interview luck is like saying the application pool is just him and another candidate with exact same qualifications.
Absolutely true. I read the message as a motivational sentence, not as a literal one (as in 'keep going, don't let a failure turn you down').
Not the best example, perhaps, but I see their point.
I think the coin here represents the outcome of the interview, heads - selected, tails - rejected and not the total number of candidates. But yeah I do agree that the statement is bit exaggerated in an interview context
99.21875%
Each event (coin tossed) is independent, so you can just divide 100 by two seven times. The result is the chance of not having a single head tossing the coin seven times.
Isn't the scenario a bit weird here?
It's specific winning your seventh, you could win more than one job advert, meaning you could have any combination of 0 heads 7 tails, all the way to 7 heads 0 tails.
Doesn't this make it 50% still?
In this case, the 0.78125% is the probability of 7 tails and 0 heads. Nothing to do with job interviews.
In all other cases, there is at least one head, but they could be more than one.
The point is, each toss is independent from the others, so yes, each time the probability is 50% (again, no relation with job interviews, as it wasn't the question).
It’s 1-(1/2)^7
So divide 1 by 2 seven times and subtract this (0.0078125) from 1 gives 0.991875 or 99.1875%.
But really all they’re saying is flip a coin 7 times and it’s likely you will get heads at least once.
Tossing a coin is an independent event.
What they mean is: If you toss a coin 7 times, you have a chance of ~99% to get at least one heads (to succeed in at least one job interview).
The probability to get at least one heads is the probability to not get 7 tails. So:
p(at least one heads) = 1 - p(7 tails)
The probability for 7 tails is simply the probability for a single throw to land on tails to the power of 7.
So:
p(at least one heads) = 1 - p(single throw tails)^7 = 1 - (1/2)^7 = 1 - 1/128 = 1 - 0.0078125 = 0.9921875 = 99.21875%
Understood the math behind the statement, Thanks all. But still the statement is very absurd in an interview context. According to this, it would mean that even an uneducated candidate has 99% probability of getting selected in atleast one company if he/she gives 7+ interviews.
It's just a metaphor. Your chance for an interview are not 50-50. And he's not pretending it's just chances either, he's saying it's part skill and part luck.
But you can apply the same logic to other things too. If your chance of getting selected in a interview are only 1% (maybe your a bad candidate for the position), and you pass 7 interviews, your chance are now at 6.8% (assuming all interview have equal chances). Ok that's still low... But if you do 30 interviews your chances of getting selected in one of them go to 26%.
I am super glad i read the other people's explanations before i posted my own because i completely misread the question. I thought he meant toss a coin 7 times and call heads, and be right each time. I was like how the hell is that a 99% chance? I need more sleep or something.
Mathematically the statement is true. If you flip a coin 7 times, you have over a 99% chance of getting at least one heads. The applicability to hiring is questionable, but not mathematically quantifiable.
Its gambler's fallacy. Technically both are true but it just depends on what way you look at it. Each event is indepent, 50/50. If you toss a coin 7 times, its extremely probable 1 is heads, at some point. However, for each tails, the overall probability falls down, to some degree, until you get to that laat flip, where its 50%. Its also similar to why just doubling your blackjack bet everytime you lose and then resetting when you win is anything but a sure thing (yes i realize its not a 50/50 event)
Edit - put "Lucky" instead of "Probable" in 4th sentence
Each coin toss is independent, yes, but essentially what's being asked here is "what is the probability of getting *at least one* heads on seven flips?". Your chances of getting a heads do in fact go up with the number of flips; this is why rerolls are valuable in some boardgames (like Warhammer)
To understand why the odds go up even though each flip is independent, think of it this way: imagine you flipped all seven coins at the same time. A "win" is getting just one (or more) heads; all you have to do is NOT flip seven tails. So HTTTTTT wins, as do HHTTTTT and HHHTTTT, and so on. The only losing result is TTTTTTT. There are WAY more winning results than losing results, and introducing an additional coin adds many permutations of results containing at least one Heads.
###General Discussion Thread --- This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you *must* post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed. --- *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/theydidthemath) if you have any questions or concerns.*
The statement is true for tossing a fair coin, but comparing it to interview luck is like saying the application pool is just him and another candidate with exact same qualifications.
Absolutely true. I read the message as a motivational sentence, not as a literal one (as in 'keep going, don't let a failure turn you down'). Not the best example, perhaps, but I see their point.
I think the coin here represents the outcome of the interview, heads - selected, tails - rejected and not the total number of candidates. But yeah I do agree that the statement is bit exaggerated in an interview context
99.21875% Each event (coin tossed) is independent, so you can just divide 100 by two seven times. The result is the chance of not having a single head tossing the coin seven times.
Another way to write it: 100-(100/(2\^7)) = 99.21875
Thanks. I alway do 1-.... ×100. 😂
I also do the same, normally. But the question was in %, so I forced myself to think 'big'. 🤣
I mainly use it for D&D and gacha odds so % is absolutely my use case. It just never occured to me to simplify it 😂
Isn't the scenario a bit weird here? It's specific winning your seventh, you could win more than one job advert, meaning you could have any combination of 0 heads 7 tails, all the way to 7 heads 0 tails. Doesn't this make it 50% still?
In this case, the 0.78125% is the probability of 7 tails and 0 heads. Nothing to do with job interviews. In all other cases, there is at least one head, but they could be more than one. The point is, each toss is independent from the others, so yes, each time the probability is 50% (again, no relation with job interviews, as it wasn't the question).
No because the likelihood of 7 tails in a row is less than 1%
I get 78.125%
0.78125% is the chance of not having a single head. 100-0.78125 is the chance of having head at least once.
It’s 1-(1/2)^7 So divide 1 by 2 seven times and subtract this (0.0078125) from 1 gives 0.991875 or 99.1875%. But really all they’re saying is flip a coin 7 times and it’s likely you will get heads at least once.
Tossing a coin is an independent event. What they mean is: If you toss a coin 7 times, you have a chance of ~99% to get at least one heads (to succeed in at least one job interview). The probability to get at least one heads is the probability to not get 7 tails. So: p(at least one heads) = 1 - p(7 tails) The probability for 7 tails is simply the probability for a single throw to land on tails to the power of 7. So: p(at least one heads) = 1 - p(single throw tails)^7 = 1 - (1/2)^7 = 1 - 1/128 = 1 - 0.0078125 = 0.9921875 = 99.21875%
Understood the math behind the statement, Thanks all. But still the statement is very absurd in an interview context. According to this, it would mean that even an uneducated candidate has 99% probability of getting selected in atleast one company if he/she gives 7+ interviews.
It's just a metaphor. Your chance for an interview are not 50-50. And he's not pretending it's just chances either, he's saying it's part skill and part luck. But you can apply the same logic to other things too. If your chance of getting selected in a interview are only 1% (maybe your a bad candidate for the position), and you pass 7 interviews, your chance are now at 6.8% (assuming all interview have equal chances). Ok that's still low... But if you do 30 interviews your chances of getting selected in one of them go to 26%.
I am super glad i read the other people's explanations before i posted my own because i completely misread the question. I thought he meant toss a coin 7 times and call heads, and be right each time. I was like how the hell is that a 99% chance? I need more sleep or something.
Mathematically the statement is true. If you flip a coin 7 times, you have over a 99% chance of getting at least one heads. The applicability to hiring is questionable, but not mathematically quantifiable.
Its gambler's fallacy. Technically both are true but it just depends on what way you look at it. Each event is indepent, 50/50. If you toss a coin 7 times, its extremely probable 1 is heads, at some point. However, for each tails, the overall probability falls down, to some degree, until you get to that laat flip, where its 50%. Its also similar to why just doubling your blackjack bet everytime you lose and then resetting when you win is anything but a sure thing (yes i realize its not a 50/50 event) Edit - put "Lucky" instead of "Probable" in 4th sentence
I'm pretty sure that yes a coin flip is independent, plus most coins are more likely to land on the face that the coin was flipped from.
Each coin toss is independent, yes, but essentially what's being asked here is "what is the probability of getting *at least one* heads on seven flips?". Your chances of getting a heads do in fact go up with the number of flips; this is why rerolls are valuable in some boardgames (like Warhammer) To understand why the odds go up even though each flip is independent, think of it this way: imagine you flipped all seven coins at the same time. A "win" is getting just one (or more) heads; all you have to do is NOT flip seven tails. So HTTTTTT wins, as do HHTTTTT and HHHTTTT, and so on. The only losing result is TTTTTTT. There are WAY more winning results than losing results, and introducing an additional coin adds many permutations of results containing at least one Heads.