Question

Out of 350350 applicants for a job, 163163 are male and 5656 are male and have a graduate degree. step 2 of 2 : if 9595 of the applicants have graduate degrees, what is the probability that a randomly chosen applicant is male, given that the applicant has a graduate degree? express your answer as a fraction or a decimal rounded to four decimal places.

Answer 1

This problem requires the knowledge of conditional probability. Conditional probability is a probability that an event B will occur given event A. We can get this probability through the formula:


`P(B|A)= (P(AandB))/(P(A))`

In the case of the problem, P(A) would be the probability that a randomly chosen applicant has a graduate degree while P(A and B) would be the probability that a randomly chosen applicant is a male AND has a graduate degree. We need to solve for P(B|A) where the chosen applicant is male given that the applicant has a graduate degree.


`P(A)= (95)/(350)=0.2714`

`P(AandB)= (56)/(350)=0.16`

`P(B|A)= (0.16)/(0.2714)=0.5895`

ANSWER: The probability that a randomly chosen applicant is male given that the applicant has a graduate degree is 0.5895 or 58.95%.