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At a small company, 40 percent of the employees are classified as junior level, and 32 percent of the employees work in department A. Of those classified as junior level, 55 percent work in department A. One employee will be selected at random. What is the probability that the selected employee works in department A and is not classified as junior level?

Answer :

Answer:

the probability that the selected employee works in department A and is not classified as junior level is;

P(A∩J') = 10% or 0.1

Step-by-step explanation:

Given;

Percent of junior level employees J = 40%

Percent of department A employees A = 32%

Percent of junior level employees in department A A∩J = 55% of J

We need to derive the percentage of the employees that are junior level and is in department A;

A∩J = 55% of J = 55% of 40% = 0.55 × 40% = 22%

A∩J = 22%

The percentage of the employees that are in department A but not junior level is;

A∩J' = A - A∩J = 32% - 22% = 10%

Therefore, the probability that the selected employee works in department A and is not classified as junior level is;

P(A∩J') = 10% or 0.1

The required probability for the given problem is 0.10 or it can be written as 10%.

Important information:

40% of the employees are classified as junior level.

32% of the employees work in department A.

55% of junior level work in department A.

Probability:

Let A and B be two events:

A: Employee is classified as junior level.

B: Employee works in department A.

The probabilities according to the given information:

P(A)=0.40

P(B)=0.32

P(A∩B)=0.55(0.40)

P(A∩B)=0.22

To find the probability that the selected employee works in department A and is not classified as junior level, we need to find P(A'∩B).

P(A'∩B) = P(B) - P(A∩B)

P(A'∩B) = 0.32 - 0.22

P(A'∩B) = 0.10

Therefore, the probability that the selected employee works in department A and is not classified as the junior level is 0.10.

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