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If a person is male, the probability that they will spend at least one night in...

If a person is male, the probability that they will spend at least one night in jail is 0.53. The probability of being male is 0.49. What is the probability of being male and having spent at least one night in jail. Show all work.

Math   Statistics-And-Probability   
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Answer #1

A : Event of a being a male

Probability of being a male : P(A) = 0.49

B : Event of spending at least one night in jail

If a person is male, the probability that they will spend at least one night in jail is 0.53 i.e P(B|A) = 0.53

Probability of being male and having spent at least one night in jail = P(A and B)

By Multiplication Theorem,

P(A and B) = P(A) P(B|A) = 0.49 x 0.53 = 0.2597

Probability of being male and having spent at least one night in jail = 0.2597

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