Question

Of all the people applying for a certain job 75% are qualified and 25% are not. The personnel manager claims that she approves qualified people 80% of the time, she approves unqualified people 30% of the time. Find the probability that a person is qualified if he or she was approved by the manager The probability is:_______.

Type an integer or decimal rounded to four decimal places as needed)

Answer 1

The probability is: 0.8889.

Explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

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

In which

P(B|A) is the probability of event B happening, given that A happened.

`P(A \cap B)` is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Approved

Event B: Qualified

Probability of a person being approved:

80% of 75%(qualified)

30% of 25%(not qualified). So

`P(A) = 0.8*0.75 + 0.3*0.25 = 0.675`

Probability of a person being approved and being qualified:

80% of 75%, so:

`P(A \cap B) = 0.8*0.75`

Find the probability that a person is qualified if he or she was approved by the manager.

`P(B|A) = (P(A \cap B))/(P(A)) = (0.8*0.75)/(0.675) = 0.8889`

The probability is: 0.8889.