Question

It is given that P(A|B) = 2/3 and P(A|notB) =1/3, find P(B|A)

Answer 1

Answer:

P(A)=1/2,P(B)=p

P(AUB)=3/5

i) Mutually exclusive P(A∩B)=0

P(AUB)=P(A)+P(B)-P(A∩B)

3/5=1/2+p-0

p=1/10

ii)Independent events P(A∩B)=P(A)*P(B)=p/2

P(AUB)=P(A)+P(B)-P(A∩B)

3/5=1/2+p-p/2

p=1/5