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."

(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