Question

A and B are two events such that P (A) ≠ 0. Find P (B|A), if (i) A is a subset of B (ii) A ∩ B = Φ

Answer 1

It is given that A and B be any events such that,

P( A )≠0

(i)

It is given that A is a subset of B then,

A∩B=A P( A∩B )=P( B∩A )=P( A )

The probability P( B|A ) is calculated as,

P( B|A )= P( A∩B ) P( A ) P( B|A )= P( A ) P( A ) =1

Therefore, the value of P( B|A ) is 1.

(ii)

It is given that,

A∩B=ϕ

So,

P( A∩B )=0

The probability P( B|A ) is calculated as,

P( B|A )= P( A∩B ) P( A ) P( B|A )= 0 P( A ) =0

Therefore, the value of P( B|A ) is 0.