Need help on the two biased coin problem

Question

Two biased coins are tossed 126 times. 36 trials are both heads and 44 trials are both tails out of

these 126 trials. Among the rest, 16 trials have head in the first coin while tail in the second coin and

30 trials with tail in the first coin and head in the second coin. Find the probability that the coin 2 gives

a tail given that the first coin gave a head.

Answer 1

Let's use the conditional probability formula: P(A | B) = P(A ∩ B) / P(B)

In this problem:

1. P(B) = the probability of of coin 1 being heads = 52/126
2. P(A ∩ B) = the probability of coin 2 being tails AND coin 1 being heads 16/126

So, our solution is P(A | B) = (16/126) / (52/126) = 16/52 = 4/13 ≈ .3077