Huntington\'s disease is a hereditary ailment caused by a recessive gene. If bot

Question

Huntington's disease is a hereditary ailment caused by a recessive gene. If both parents carry the gene but do not have the disease, there is a 0.25 probability that an offspring will fall victim to the condition. A newly wed couple find through genetic testing that they both carry the gene (but do not have the disease). If they intend to have five children, find the probability of each event. (Round your answers to five decimal places.)

(a) At least one child gets the disease.


(b) At least four of the children get the disease.

Explanation / Answer

p = 0.25

n = 5

This is a binomial distribution

P(X = x) = 5Cx * 0.25x * (1 - 0.25)5-x

a) P(X > 1) = 1 - P(X = 0)

                   = 1 - 5C0 * 0.250 * 0.755

                   = 1 - 0.23730

                   = 0.76270

b) P(X > 4) = P(X = 4) + P(X = 5)

                   = 5C4 * 0.254 * 0.751 + 5C5 * 0.255 * 0.750

                   = 0.01563

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