Question

Out of 431 applicants for a job, 164 have over 10 years of experience, and 141 have over 10 years of experience and have a graduate degree. Consider that 155 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?

a) 0.904
b) 0.875
c) 0.919
d) 0.966

Answer 1

The probability that a randomly chosen applicant has over 10 years of experience, given that the applicant has a graduate degree, is
`\( (141)/(155) \)` or approximately 0.919. Therefore, the correct answer is c) 0.919.

Step-by-step explanation:

In this problem, we are dealing with conditional probability, specifically the probability of having over 10 years of experience given that the applicant has a graduate degree. The formula for conditional probability is given by:

`\[ P(A|B) = (P(A \cap B))/(P(B)) \]`

In this context, let's define:

- (A) as the event of having over 10 years of experience,

- (B) as the event of having a graduate degree.

We are given that
`\( P(A) = (164)/(431) \)` (applicants with over 10 years of experience),
`\( P(A \cap B) = (141)/(431) \) \\`(applicants with over 10 years of experience and a graduate degree), and
`\( P(B) = (155)/(431) \)` (applicants with a graduate degree).

Now, applying the formula:

`\[ P(A|B) = (P(A \cap B))/(P(B)) \]`

`\[ P(A|B) = ((141)/(431))/((155)/(431)) = (141)/(155) \]`

Therefore, the probability that a randomly chosen applicant has over 10 years of experience, given that the applicant has a graduate degree, is
`\( (141)/(155) \)` or approximately 0.919. This aligns with option c) 0.919 as the correct answer.

Answer 2

The probability that a randomly chosen applicant has over 10 years of experience, given that the applicant has a graduate degree, is calculated by dividing the number of applicants with both qualifications by the number of applicants with a graduate degree, resulting in a probability of approximately 0.91.

Step-by-step explanation:

The student is asking about the probability that a randomly chosen applicant has over 10 years of experience, given that the applicant has a graduate degree. To find this probability, we use the formula for conditional probability, which is the probability of event A given event B has occurred equals the probability of both events A and B occurring divided by the probability of event B.

To compute this, we know that there are 141 applicants with over 10 years of experience and a graduate degree, and there are 155 applicants with a graduate degree. So the probability is calculated as:

1. Calculate the conditional probability: Probability(Event A | Event B) = P(A & B) / P(B)
2. Substitute the given values: P(>10 years experience | graduate degree) = 141 / 155
3. Perform the division to find the probability.

Performing the division, 141 / 155 = 0.9097, which can be rounded to two decimal places, giving us a probability of 0.91. This is closest to option c) 0.919, which is our answer.