Question

A manager has available a pool of 8 employees who could be assigned to a​ project-monitoring task. 3 of the employees are women and 5 are men. 4 of the men are brothers. The manager is to make the assignment at random so that each of the 8 employees is equally likely to be chosen. Let A be the event​ "chosen employee is a​ man" and B the event​ "chosen employee is one of the​ brothers."

a. Find the probability of A.

b. Find the probability of B.

c. Find the probability of the intersection of A and B.

Answer 1

Given that

Total Employees = 8

women = 3

Men = 5

4 of the men are brothers

Let A be the event​ "chosen employee is a​ man"

Let B the event​ "chosen employee is one of the​ brothers."

a) Probability of event A = No. of Men / Total Employees

P(A) = 5/8 = 0.625

b) Probability of event B = probability of chosen employees is one of the brothers

P(B) = No of men are brothers / Total Employees

P(B) = 4/8 = 1/2 =0.5

c) probability of the intersection of A and B.

A= 5 men B =4men of brother

Intersection of  A and B is 4 Men

P( A B) = Intersection of  A and B / Total employees

P( A B) =  4/8 = 0.5