A report of a study shown that, from a randomly selected 100 individuals partici

Question

A report of a study shown that, from a randomly selected 100 individuals participated in the study, 30 people had been exposed to a risky environment and had disease A, and 10 people that had been exposed to this environment did not have the disease A. Also, 10 people that had been not exposed to this risky environment had disease A, and 50 people who had been not exposed to this environment did not have the disease A. If a person with disease A is selected at random from this study, what is the probability that this person had been exposed to the risky environment?

Explanation / Answer

Baye's Theorem: P(A | B) = P(A&B)/P(B)

P(person has been exposed to risky environment | person is having disease A)

= P(person has been exposed to risky environment and is having disease A) / P(person is having disease A)

= 30/(30+10)

= 30/40

= 0.75

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