Question

A survey showed that the probability that an employee gets placed in a job that is suitable for the employee is 0.65. A psychometric test consultant claimed that he could help place any employee in a suitable job based on the result of a psychometric test. An employee working in a particular company decides to take this test. The test has an accuracy rate of 70%. This data is represented in the tree diagram.

Select the correct answer. Which of these probability values fit the tree diagram?
A. P(A) = 0.35, P(B) = 0.65, P(C) = 0.70, P(D) = 0.30, P(E) = 0.30, P(F) = 0.70
B. P(A) = 0.35, P(B) = 0.65, P(C) = 0.70, P(D) = 0.30, P(E) = 0.70, P(F) = 0.30
C. P(A) = 0.35, P(B) = 0.65, P(C) = 0.30, P(D) = 0.70, P(E) = 0.70, P(F) = 0.30
D. P(A) = 0.65, P(B) = 0.35, P(C) = 0.70, P(D) = 0.30, P(E) = 0.30, P(F) = 0.70

Answer 1

A survey shows that the probability that an employee gets placed in a suitable job is 0.65.

A. P(A) = 0.35, P(B) = 0.65, P(C) = 0.70, P(D) = 0.30, P(E) = 0.30, P(F) = 0.70

Step-by-step explanation:

So, the probability he is in the wrong job is 0.35.

The test has an accuracy rate of 70%.

So, the probability that the test is inaccurate is 0.3.

Thus, the probability that someone is in the right job and the test predicts it wrong is 0.65*0.3=0.195

The probability that someone is in the wrong job and the test is right is 0.35*0.7= 0.245