Compute At-least Probabilities
-A human gene carries a certain disease from the mother to the child with a probability rate of 35%. That is, there is a 35% chance that the child becomes infected with the disease. Suppose a female carrier of the gene has five children. Assume that the infections of the five children are independent of one another. Find the probability that at least one of the children get the disease from their mother.
A) 0.884
B) 0.062
C) 0.312
D) 0.116

Question

Quizplus · Accepted Answer

The probability that at least one child gets the disease is 1 minus the probability that none of the children get the disease. The probability that a child does not get the disease is 65% (100% - 35%). For five children, this is $0.65^5$. Thus, the probability that at least one child gets the disease is $1 - 0.65^5 = 0.884$.

Compute At-Least Probabilities -A Human Gene Carries a Certain Disease from the Mother