After studying a couple’s family history, a doctor determines that the probabili

Question

After studying a couple’s family history, a doctor determines that the probability of any child born to this couple having a gene for disease X is 25%. If the couple has 3 children, what is the probability that at least one of their children has the disease? After studying a couple’s family history, a doctor determines that the probability of any child born to this couple having a gene for disease X is 25%. If the couple has 3 children, what is the probability that at least one of their children has the disease?

Explanation / Answer

Probability that at least one of the children has the disease = 1 - probability that none of the children has the disease.

Probability that a child has the disease =0.25

Probability that a child doesn't have the disease = 1-0.25 = 0.75

Probability that all 3 children don't have the disease = 0.75 x 0.75 x 0.75 = 0.42188 (since the events are independent of each other, i.e., any child having or not having the disease is independent of any other child having or not having the disease).

Probability that at least one of the children has the disease = 1 - 0.42188 = 0.57812

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