The entertainment sports industry employs athletes, coaches, referees, and related workers. Of these, 0.35 work part time and 0.52 earn more than $20,540 annually. If 0.3 of these employees work full time and earn more than $20,540, what proportion of the industry's employees are full time or earn more than $20,540

Step-by-step explanation:

let A be the event that employees work full time

Pr(A) =  1 - 0.35=  0.65   (  given : Pr( employee work part time) = 0.35)

let B be the event that employees earn more than $20,540

Pr(B) =  0.52

Pr(  employee work full time and earn more than $20,540) =  0.3

Pr( A∩B) = 0.3

we know that

Pr( employee work full time or earn more than $20,540) = Pr( A∪B)

Also

Pr( A∪B)   =  Pr(A)  + Pr(B)  -  Pr(A∩B)

                   =  0.65   + 0.52  -   0.3

                    =    1.17    -   0.30

                     =    0.87