Question

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."

Answer 1

Answer:

(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