What Is the Probability Both Children Will Have the Same Eye Color and Gender?

[jaxnnux]

Hello Gentlemen,

Here's a statistical question for you:

A man and a woman mate to produce a child that either has blue eyes (B) or green eyes (b), where blue eyes are dominant to green eyes.

As you remember from biology, there are 3 different possibilities for the genotype - BB, Bb, or bb.

The probabilities are 1:2:1 for BB:Bb:bb.

Thus, the chance for the child to have blue eyes is 3/4 and green eyes is 1/4.

Ok, I'm getting to the question now. The couple decides to have 2 children. What is the probability that the 2 children will have the same appearance and be of the same sex?

Here's what I think the answer is:

green eyes: (0.5*0.5*0.25*0.25)*100% = 1.5%
blue eyes:
(0.5*0.5*0.75*0.75)*100% = 14.1%

Is this correct? Thanks.

 

[EnumaElish]

Prob(same sex) = P(boy)²+P(girl)² = 2(0.5)² = 2*0.25 = 0.5.

Blue boys = (0.5*0.75)² = Blue girls

green boys = (0.5*0.25)² = green girls

Blue boys or blue girls = 2(0.5*0.75)²
green boys or green girls = 2(0.5*0.25)²