Question

If P(A) = 0.5, P(B | A) = 0.40, P(A ∪ B) = 0.35, then P(B) =

a) 0.05
b) 0.33
c) 0.25
d) 0.80
e) 0.55
f) 0.14
g) 0.15
h) 0.20
i) None of the listed answers

Answer 1

Ans will be (a) 0.05

Explanation,

Since P(AB) = P(A) + P(B) - P(AB) (1)

And P(AB) = P(A)*P(B|A)(2)

Now, put the value of equation (2) in equation (1), we get

P(AB) = P(A) + P(B) - P(A)*P(B|A)

P(B)= P(AB) - P(A) + P(A)*P(B|A)

P(B)= 0.35 - 0.5 + (0.5*0.4)

P(B)=0.05