DATA ANALYSIS ENGINEERING

Question

A male fruit fly is equally likely to carry alleles a or b on the X chromosome. Allele a is lethal

for females, so if the male fruit fly carries a, all of its offspring will be male. If the male fly

carries allele b, then each offspring is equally likely to be male or female. If we observe

three offspring and all are male, what is the conditional probability that the male fly carries

allele a?

Answer 1

P(carry allele a | 3 male offspring) = P(carry allele a and 3 male offspring)/P(3 male offspring) =

P(3 male offspring| carry allele a)P(carry allele a)/(P(3 male offspring| carry allele a)P(carry allele a) + P(3 male offspring| carry allele b)P(carry allele b))

P(carry allele a) = P(carry allele b) = 1/2

P(3 male offspring| carry allele a) = 1

P(3 male offspring|carry allele b) = (1/2)³ = 1/8

Then,

P(3 male offspring| carry allele a)P(carry allele a)/(P(3 male offspring| carry allele a)P(carry allele a) + P(3 male offspring| carry allele b)P(carry allele b)) =

1 * 1/2/(1 * 1/2 + 1/8 * 1/2) = 1/2/(9/16) = 8/9