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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?

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  • $\begingroup$ 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. $\endgroup$ – koon93 May 24 '17 at 3:51
  • $\begingroup$ Could you check my answer :D I need reputation :D $\endgroup$ – Eric Lee May 24 '17 at 4:01
  • $\begingroup$ Brown is $\color{#f00}{dominant}$ as compared to blue. Then, why the factors have $\color{#f00}{equal}$ probabilities ? !!!. $\endgroup$ – Felix Marin May 24 '17 at 4:32
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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: $$\frac{2}{3}\cdot \frac{1}{2} + \frac{1}{3}\cdot 0 = \boxed{\frac{1}{3}}$$

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  • $\begingroup$ Oops I read "Help me start with this question" part a little late :P Well... I guess you get a free answer??? $\endgroup$ – Eric Lee May 24 '17 at 3:55
  • $\begingroup$ Also by "have", I mean "has a genotype of" $\endgroup$ – Eric Lee May 24 '17 at 3:56

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