probability question

Question

The probability of a fish weighing more than 20kg is 0.78. A ship catches 15 fish in the first hour.The probability that the first fish caught weighs more than 20kg given at least 8 out of the 15 fish weigh more than 20kg is?

Answer 1

P(first fish caught weighs more than 20 kg|at least 8 of 15 weigh more than 20 kg) =

P(first fish caught weights more than 20 kg and at least 8 of 15 weigh more than 20 kg)/P(at least 8 of 15 weigh more than 20 kg) =

P(first fish caught weights more than 20 kg and at least 7 of 14 others weigh more than 20 kg)/P(at least 8 of 15 weigh more than 20 kg) =

P(first fish caught weights more than 20 kg and at most 7 of 14 others weigh less than or equal to 20 kg)/P(at most 7 of 15 weigh less than or equal to 20 kg)

1 - .78 = .22

.78 * binom.dist(7,14,.22,1)/binom.dist(7,15,.22,1) = .7826