Question

P(B|A)=P(B)*P(A|B)/P(A) <---Formula

Consider 3 coins, 2 that are fair and 1 that is not. Assume that the unfair coin has a 3/4 probability of landing heads and a 1/4 probability of landing tails.

Question: What is the probability that the coin you have chosen out of these 3 is fair, given that you flip 5 heads in a row?
I need help understanding this... It is really confusing

Answer 1

P(B|A) is the probability of B, given A.

Put in this context, you might write it this way: P(Coin is fair | flipped 5 heads in a row) = P(Coin is fair) * P(Flipped 5 heads in a row | coin is fair) / P(flipped 5 heads in a row)

Answer 2

So how would you multiply and devide that? would you use the 3/4 and 1/4 values in the equation?

Answer 3

In this case, since 1 coin is unfair and 2 are fair,

P(Coin is fair) = 2/3
P(flipped 5 heads in a row | coin is fair) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2

That's the easiest part. The only mildly confusing part would be
P(flipped 5 heads in a row)

but we can find that this way:

P(flipped 5 heads in a row) = 2/3 * ( 1/2 * 1/2 * 1/2 * 1/2 *1/2) + 1/3 * (3/4 * 3/4 * 3/4 * 3/4 * 3/4)

Answer 4

In the last part, the probability is like a weighted average -- 2/3 from the fair coins, and 1/3 from the unfair coin.

Answer 5

okay I see

Answer 6

Thank you!

Answer 7

Sure, no problem.