SOLUTION: 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 w

Question 1008135: 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.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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.)
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Binomial Problem with n = 5 and p(victim) = 0.25 ; p(not victim) = 0.75
(a) At least one child gets the disease.
P(at least one) = 1 - P(none)
P(x >=1) = 1 - 0.75^5 = 0.7627
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(b) At least four of the children get the disease.
P(4<= x <=5) = 1 - binomcdf(5,0.25,3) = 0.0156
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Cheers,
Stan H.
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