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# Three people have been exposed to a certain illness. Once exposed, a person has a 50–50 chance of actually becoming ill. a. What is the probability that exactly one of the people becomes ill? b. What is the probability that at least two of the people becomes ill? c. What is the probability that none of the three people becomes ill?

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Exactly one: $\dfrac{3}{8} = 37.5\%$

There are 8 possible cases: (I,I,I),(H,H,H),(I,I,H),(I,H,H),(I,H,I),(H,I,I),(H,H,I),(H,I,H) where H is healthy, and I is ill. There are 3 cases in which exactly one is ill. Calculated by the formula P(A) = Useful Outcomes / All Outcomes we get the result.

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