Probability...?

Question

The independent events A, B are such that P(A) = 0.4 and P(A U B)=0.88. Find

a) P(B)

b) the probability that either A occurs of B occurs but NOT both

Answer 1

a) since P of AUB = PA+PB-(PAPB)
0.88 = 0.4 + PB - (0.4PB)
0.88 = 0.4 + 0.6 PB
0.48 = 0.6 PB
PB = 0.8
b) the probability of either A or B but not both is
PAUB - PAPB
= 0.88 - (0.4)(0.8)
= 0.56

Answer 2

a)P(B)=P(AUB)-P(A)=0.48
b)This is called mutual exclusivity =
P(AUB)=0.88