Question

Let A, B be events of a sample space S with probabilities P(A) = 0.25, P(B) = 0.35 and P(A∪B) = 0.4. Calculate (i) P(A|B) ,(ii) P(B|A), (iii) P(A∩B), (iv) P(A|B).

Answer 1

Using addition rule,

P(A B) = P(A) + P(B) - P(A B)

So,

P(A B) = P(A) + P(B) - P(A B)

= 0.25 + 0.35 - 0.4

= 0.2

a)

P(A | B) = P(A B) / P(B)

= 0.2 / 0.35

= 0.5714

b)

P(B | A) = P(A B) / P(A)

= 0.2 / 0.25

= 0.8

c)

P(A B) = 0.2

d)

P(A | B) = 0.5714 (Calculated in part a)