Question

Out of 450 applicants for a job, 212 are female and 55 are female and have a graduate degree. If 93 of the applicants have graduate degrees, what is the probability that a randomly selected applicant is female given that the applicant has a graduate degree?

Answer 1

The probability that a randomly selected applicant is female given that the applicant has a graduate degree is approximately 0.5914.

Step-by-step explanation:

To find the probability that a randomly selected applicant is female given that the applicant has a graduate degree, we can use the concept of conditional probability.

Let's first find the probability of an applicant being female and also having a graduate degree. We are given that there are 55 applicants who are female and have a graduate degree out of 450 applicants. So the probability of an applicant being female and having a graduate degree is 55/450.

Next, we need to find the probability of an applicant having a graduate degree. We are given that there are 93 applicants with graduate degrees out of 450 applicants. So the probability of an applicant having a graduate degree is 93/450.

Finally, we can use the formula for conditional probability:

P(Female|Graduate Degree) = P(Female and Graduate Degree) / P(Graduate Degree)

Substituting the values we found:

P(Female|Graduate Degree) = (55/450) / (93/450) = 55/93 ≈ 0.5914