It has been reported that men are more likely than women to participate in online auctions. In a recent survey, 65% of respondents reported that they had participated in an
Online auction. In this same survey, 45% of respondents were men and 38% were men
Who had participated in online auctions. What is the probability that a respondent had
Participated in an online auction given that he is male?
A) 0.38
B) 0.84
C) 0.62
D) 0.45
E) 0.55

Question

Quizplus · Accepted Answer

We need to use Bayes' Theorem to find the probability of a respondent having participated in an online auction given that he is male. Bayes' Theorem states that:

P(A | B) = P(B | A) * P(A) / P(B)

where A is the event that a respondent has participated in an online auction, B is the event that the respondent is male, P(A | B) is the probability of A given B, P(B | A) is the probability of B given A, P(A) is the overall probability of A, and P(B) is the overall probability of B.

We are given that P(A) = 0.65 (65% of respondents participated in online auctions) and P(B) = 0.45 (45% of respondents were male).

We need to find P(B | A), the probability of a respondent being male given that they participated in an online auction. We are given that 38% of respondents were men who had participated in online auctions, so P(B and A) = 0.38. Using the formula for conditional probability, we have:

P(B | A) = P(B and A) / P(A) = 0.38 / 0.65 = 0.5846 (rounded to four decimal places)

Therefore, the probability of a respondent having participated in an online auction given that he is male is approximately 0.5846, which is closest to answer choice B (0.84).

It Has Been Reported That Men Are More Likely Than