Q#42: Probablity of hair colors

Assume that hair color is a genetically inherited trait controlled by one gene with two alleles. You can assume that Brown hair and Red hair pose a 50/50 chance of inheritance when mixed. A brown-haired man and a red-haired woman have 3 children. The first has red hair. What is the probability that all three children will have red hair?

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ANSWER

This question tests our understanding of basic probability theory. Since the hair color of the 3 children are independent, the probability that all three children will have red hair is simply multiplication of the probabilities each will have red hair. The only trick here is that we already know the first child has red hair, so his/her probability is 1 then the next two kids probability of red hair is 0.5 each. 1 x 0.5 x 0.5 = 0.25 or 25%.