Question

The division of the company where you work has 85 employees. Thirty of them are bilingual, and 37% of the bilingual employees have a graduate degree. If an employee of this division is randomly selected, what is the probability that the employee is bilingual and has a graduate degree

Answer 1

Explanation:

Hello!

You have two events.

A: The employee is bilingual.

The probability of the employee being bilingual is P(A)= 30/85= 0.35

And

B: The employee has a graduate degree.

Additionally, you know that the probability of an employee having a graduate degree given that he is bilingual is:

P(B/A)= 0.37

You need to calculate the probability of the employee being bilingual and having a graduate degree. This is the intersection between the two events, symbolically:

P(A∩B)

The events A and B are not independent, which means that the occurrence of A modifies the probability of occurrence of B.

Applying the definition of conditional probability you have that:

P(B/A)= [P(A∩B)]/P(A)

From this definition, you can clear the probability of the intersection between A and B

P(A∩B)= P(B/A)* P(A)= 0.37*0.35= 0.1295≅ 0.13

I hope it helps!