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28 April, 00:14

A recent survey asked 100 randomly selected adult Americans if they thought that women should be allowed to go into combat situations. Here are the results:

Gender Yes No

Male 32 18

Female 8 42

(a) Find the probability of a "Yes" answer, given that the person was a female.

(b) Find the probability that the respondent was a male, given that the response was a "No."

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  1. 28 April, 03:37
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    (a) The probability of a "Yes" answer, given that the person was a female is 0.16

    (b) The probability that the respondent was a male, given that the response was a "No" is 0.3

    Step-by-step explanation:

    This problem can be solved using the definition of conditional probability

    P (B|A) = P (A∩B) / P (A)

    (a) In this case, event A is that the person is female and event B is that the answer of the person is "Yes".

    P ("Yes" | Female) = P (Female ∩ "Yes") / P (Female)

    P ("Yes" | Female) = (8/100) / (50/100)

    P ("Yes" | Female) = 8/50

    P ("Yes" | Female) = 0.16

    (b) In this case, event A that the answer of the person is "No" and event B is that the person is male.

    P (Male | "No") = P ("No" ∩ Male) / P ("No")

    P (Male | "No") = (18/100) / (60/100)

    P (Male | "No") = 18/60

    P (Male | "No") = 0.3
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