Question

Out of 419 applicants for a job 126 have over 10 years experience and 83 have over 10 years experience and have a graduate degree. Consider that 142 of the applicants have graduate degrees. What is the probability that a randomly chosen applicant has over 10 years of experience, given that the applicant has a graduate degree?

Answer 1

The probability that a randomly chosen applicant has over 10 years of experience, given that the applicant has a graduate degree, is calculated using conditional probability. It is approximately 58.45%, found by dividing the number of applicants with both over 10 years of experience and a graduate degree (83) by the total number of applicants with a graduate degree (142).

Step-by-step explanation:

The student asked what the probability is that a randomly chosen applicant has over 10 years of experience, given that the applicant has a graduate degree. Out of 419 applicants, 126 applicants have over 10 years of experience, and 83 of these also have a graduate degree. Since 142 applicants have graduate degrees in total, we can calculate the conditional probability. The formula for conditional probability is P(A|B) = P(A ∩ B) / P(B), where A is the event that an applicant has over 10 years of experience and B is the event that an applicant has a graduate degree.

To find the probability that a randomly chosen applicant has over 10 years of experience given they have a graduate degree:

1. Compute the joint probability of the two events happening together (both having over 10 years of experience and a graduate degree), which is P(A ∩ B) = 83/419.
2. Compute the probability of an applicant having a graduate degree, which is P(B) = 142/419.
3. Divide the joint probability by the probability of an applicant having a graduate degree: P(A|B) = (83/419) / (142/419).
4. Simplify the fraction: P(A|B) = 83/142.

This results in the probability of approximately 0.5845, or 58.45%, that an applicant has over 10 years of experience given they have a graduate degree.