Independent events, A and B where P(B) = 0.25 and P(A ∩ B) = 0.15. Find P(B' l A) and P(A' ∩ B')

Answer 1

IA and B are the only events in the Sample Space,

P(B)=0.25

P(A∩B)=0.15

P(A∪B)=P(A) +P(B) -P(A∩B)

Let probability of union of A and B equal 1

1=P(A) + 0.25 - 0.15

1=P(A) +0.10

1-0.10=P(A)

0.90=P(A)

P(B´⌊A)=P(A∩B´)/P(A)

P(A∩B´) + P(A∩B)=P(A)

P(A∩B´) +0.15=0.90

P(A∩B´)=0.75

P(B´⌊A)=0.75/0.90 or 5/6

(A´∩B´)´=A∪B

P(A´∩B´)=1-P(A∪B)

P(A´∩B´)=1-1

P(A´∩B´)=0

Answer 2

If A and B are independent, then A and B' are independent too, and A' and B' are independent. This means that

P(A ∩ B) = P(A) * P(B)

P(B' | A) = P(B')

P(A' ∩ B') = P(A') * P(B')

Hope, you can finish the rest yourself.