Answer
Let P denote should be paid, N denotes not be paid, A denotes student athlete and B denotes nonathlete
i. P(P) = $\frac{300}{400}$ = 0.75
ii. P(P|B) = $\frac{210}{300}$ = 0.7
iii. P(A ∩ P) =$\frac{90}{400}$ = 0.225
iv. P(B U N) = [P(B) + P(N) ]- P(B∩N)
= $\frac{300+100-90}{400}$
=0.775
b. P(A) = $100/400$
=0.25
P(A|P) = $90/300$
=0.3
The events student athlete and should be paid are not independent, because P(A) is not equal to P(A|P).
They are not mutually exclusive, because $P(A∩P) \ne 0 $
Work Step by Step
See above.
