Answer:
We can use Bayes' theorem to solve this problem. Let A be the event that an applicant has over 10 years of experience, and let B be the event that an applicant has a graduate degree. We want to find the conditional probability P(B|A), which is the probability that an applicant has a graduate degree given that they have over 10 years of experience.
Bayes' theorem states that:
P(B|A) = P(A|B) * P(B) / P(A)
We are given that 229 applicants have over 10 years of experience, so P(A) = 229/423. We are also given that 62 applicants have over 10 years of experience and a graduate degree, so P(B and A) = 62/423.
To find P(B), we need to consider all applicants, regardless of their experience level. We are not given this information directly, but we can use the fact that the sum of the probabilities of all possible outcomes is 1:
P(B and not A) + P(B and A) = P(B)
We can rearrange this equation to solve for P(B):
P(B) = P(B and A) + P(B and not A)
P(B) = 62/423 + P(B and not A)
We can find P(B and not A) by subtracting P(B and A) from P(B):
P(B and not A) = P(B) - P(B and A)
P(B and not A) = 1 - P(not B) - P(A and not B)
P(B and not A) = 1 - (194/423) - (167/423)
P(B and not A) = 62/423
Now we have all the information we need to apply Bayes' theorem:
P(B|A) = P(A|B) * P(B) / P(A)
P(B|A) = (62/229) * (62/423) / (229/423)
P(B|A) = 0.152
Therefore, the probability that a randomly chosen applicant has a graduate degree given that they have over 10 years of experience is 0.152 or approximately 15.2%.