Question

Problem 2 (Unit 4). A company hires graduate students who apply for a job from three local universities. The following table summarizes the proportions of male and female applicants (graduate students). Universities Graduates A B C. Female (F) .08 .20 .10 Male (M) .19 .30 .13 Answer the following questions (show your calculations). a. If an applicant is chosen randomly, what is the probability the chosen applicant is male? b. What is the probability that a randomly chosen applicant is male, given that the chosen applicant is from university A? c. What is the probability that a randomly chosen applicant is from university B, given that the chosen applicant is female? d. Is gender independent of which university the applicant is graduated from?

Answer 1

a. To find the probability that a randomly chosen applicant is male, we sum up the proportions of male applicants from each university: 0.19 + 0.30 + 0.13 = 0.62.

b. To find the probability that a randomly chosen applicant is male, given that the chosen applicant is from university A, we divide the proportion of male applicants from university A by the total proportion of applicants from university A: 0.19 / (0.08 + 0.19) = 0.7037.

c. To find the probability that a randomly chosen applicant is from university B, given that the chosen applicant is female, we divide the proportion of female applicants from university B by the total proportion of female applicants: 0.20 / (0.08 + 0.20 + 0.10) = 0.5714.

d. To determine if gender is independent of the university the applicant graduated from, we compare the probabilities of being male or female across all universities. If the probabilities are the same, then gender is independent of the university. In this case, the probabilities are not the same, so gender is not independent of the university the applicant graduated from.