Suppose a genetic trait is inherited via the Y chromosome so

Suppose a genetic trait is inherited via the Y chromosome, so that a male offspring of a father with the trait has a 25% chance of inheriting it but a female offspring cannot inherit it. If 45% of all births in a certain population are male, what is the probability that a father with the trait has two offspring who both have the trait? You can assume that offspring genders are independent events

Solution

the probability is intersection of two events - 1) both offsprings are male with prob 0.45 for each male birth because only males can inheirt the trait

2) both males have inherited the trait with prob 0.25

P = 0.45 x 0.25 x 0.45 x 0.25 = 0.01265