Question

Let P(A)=0.4 , P(B)=0.7, P(AUB)=0.8. Find:
1) P(Bc)=



2) P(A-B)=





3) P(AUBc)=



4) P(B/A)=



5) P(Bc/A)=

Answer 1

Answer:

P(A∪B)+P(A∩B)=P(A)+P(B)=0.7+0.2=0.9

P(A∩B)=0.2=P(A)P(B)

P(B)=0.9-P(A), P(A)(0.9-P(A))=0.2,

P^2(A)-0.9P(A)+0.2=0

P(A)=½(0.9±√[0.81–0.8])={0.5,0.4}

P(B)=0.9-P(A)={0.4,0.5}, as P(A)＞P(B):

P(A)=0.5, P(B)=0.4

Answer : P(A)=0.5, P(B)=0.4