Eye colour genetics.

Brown eye genes is dominant vs. blue eye genes. A person inherits one factor from each parent with equal probability. If both my parents and I have brown eyes and my brother and my wife have blue eyes, what is the probability that my child has blue eyes?

• I dont really know where to start with this question. If someone is able to give an idea as to how to start approaching this question then that would be great. – koon93 May 24 '17 at 3:51
• Could you check my answer :D I need reputation :D – Eric Lee May 24 '17 at 4:01
• Brown is $\color{#f00}{dominant}$ as compared to blue. Then, why the factors have $\color{#f00}{equal}$ probabilities ? !!!. – Felix Marin May 24 '17 at 4:32

Let's set the recessive genes as $r$ and Dominant as $R$. If both your parents have brown eyes but you brother has blue eyes, then both of your parents have to be $Rr$. Drawing a punnet square, you have a $\frac{2}{3}$ chance of being $Rr$ and a $\frac{1}{3}$ chance of being $RR$.
Your wife has $rr$ genes, as she has blue eyes. If you have $Rr$ genes, then your child has $\frac{1}{2}$ chance of having blue eyes, whereas if you have $RR$ genes, you have $0$.
Adding these cases, you get: $$\frac{2}{3}\cdot \frac{1}{2} + \frac{1}{3}\cdot 0 = \boxed{\frac{1}{3}}$$