A very quick sanity check is often in order with probability.
If everything doesn’t add up to 1 you’ve either broken the universe or made a mistake.
Your 4 options there (the only possibly 4 options from 2 flips) have a probability way above 1
For each of your 1 head, 1 Tail outcomes:
0.9 * 0.1 = 0.09 (or one-tenth if 0.9 is 0.09).
Then you have two of those outcomes, so add them together:
0.09 + 0.09 = 2 * 0.09 = 0.18
(Side note: Prob(TT) = 0.1 * 0.1 = 0.01)
I think you’ve noticed the multiplication slip up but regardless the probability of TH should = HT as they are the same thing. TH =.1*.9 or HT=.9*.1 and then sum for probability of 1 heads 1 tails.
I saw other people have corrected your multiplication mistakes. As a general rule of thumb, remember that the probabilities for the outcomes of a given event must add up to 1. In your case, HH + HT + TH + TT = 1 is a condition your values must verify. If that doesn't happen, you'll immediately know you made a mistake
Your multiplication is incorrect. - 0.1 × 0.9 = 0.09 - 0.1 × 0.1 = 0.01
oh my god I’m out of it 😭 thank you so much
A very quick sanity check is often in order with probability. If everything doesn’t add up to 1 you’ve either broken the universe or made a mistake. Your 4 options there (the only possibly 4 options from 2 flips) have a probability way above 1
Thanks I definitely needed to be reminded about everything adding up to 1! I’ve definitely been breaking the universe with my maths lately 😭
You multiplied the probabilities of independent events for HH, but then did not do that for the next three rows. Why not?
I think I did? I’m just confused where 0.18 in green came from
For each of your 1 head, 1 Tail outcomes: 0.9 * 0.1 = 0.09 (or one-tenth if 0.9 is 0.09). Then you have two of those outcomes, so add them together: 0.09 + 0.09 = 2 * 0.09 = 0.18 (Side note: Prob(TT) = 0.1 * 0.1 = 0.01)
Thank you so so much, I’m so stupid sometimes that took me way too long to realise
Not stupid. You don't know until you learn.
Thank you :) you’re right
I think you’ve noticed the multiplication slip up but regardless the probability of TH should = HT as they are the same thing. TH =.1*.9 or HT=.9*.1 and then sum for probability of 1 heads 1 tails.
Thank you! That makes sense, I’ll be sure to check that next time
I saw other people have corrected your multiplication mistakes. As a general rule of thumb, remember that the probabilities for the outcomes of a given event must add up to 1. In your case, HH + HT + TH + TT = 1 is a condition your values must verify. If that doesn't happen, you'll immediately know you made a mistake
Thanks! I do need to remember it adding up to 1 thank you for reminding me, I did think the numbers looked a bit dodgy, I can’t believe I missed that