Question

If A and B are two events such that A ⊂ B and P (B) ≠ 0, then which of the following is correct? A. B. C. D. None of these

Answer 1

Given, A⊂B then . A∩B=A.

Thus, P( A∩B )=P( A )

Now, probability if both A and B event happens,

P( A|B )= P( A∩B ) P( B ) P( B )= P( A∩B ) P( A|B ) P( B )= P( A ) P( A|B )                     [ P( A∩B )=P( A ) ]

Also,

0<P( B )≤1 0< P( A ) P( A|B ) ≤1 0×P( A|B )<P( A )≤1×P( A|B ) 0<P( A )≤P( A|B )

Therefore,

P( A|B )≥P( A )

Hence, option (C) is correct.