Muscular dystrophy is a genetic disease caused by a mutation on the X chromosome. During reproduction this mutation arises spontaneously on each of the X chromosomes of the parents, independently and with probability = 0.78. We can therefore view the production of a child as consisting of two probabilistic experiments. First, one of the two sex chromosomes is chosen with equal probability from each parent. Second, for each X chromosome that is chosen, the muscular dystrophy mutation arises independently with probability μ. All male children carrying the mutation will develop muscular dystrophy, whereas only females whose X chromosomes both carry the mutation will develop the disease. What is the probability that a child will develop the disease? Round your answer to five decimal places

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Muscular dystrophy is a genetic disease caused by a mutation on the X chromosome. During
reproduction this mutation arises spontaneously on each of the X chromosomes of the
parents, independently and with probability : 0.78. We can therefore view the production
of a child as consisting of two probabilistic experiments. First, one of the two sex
chromosomes is chosen with equal probability from each parent. Second, for each X
chromosome that is chosen, the muscular dystrophy mutation arises independently with
probability u. All male children carrying the mutation will develop muscular dystrophy,
whereas only females whose X chromosomes both carry the mutation will develop the
disease. What is the probability that a child will develop the disease? Round your answer to
five decimal places.
Transcribed Image Text:= Muscular dystrophy is a genetic disease caused by a mutation on the X chromosome. During reproduction this mutation arises spontaneously on each of the X chromosomes of the parents, independently and with probability : 0.78. We can therefore view the production of a child as consisting of two probabilistic experiments. First, one of the two sex chromosomes is chosen with equal probability from each parent. Second, for each X chromosome that is chosen, the muscular dystrophy mutation arises independently with probability u. All male children carrying the mutation will develop muscular dystrophy, whereas only females whose X chromosomes both carry the mutation will develop the disease. What is the probability that a child will develop the disease? Round your answer to five decimal places.
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