If A and B are two events such that `P(A)=1/4, P(B)=1/2a n d\ P(AnnB)=1/8` , find `P` (not A and not B).

Explanation

We have, `P(A)=frac{1}{2}` and `P(A cap B)=frac{1}{8}`


P( not an A and not on B)`=P(A^{prime} cap B^{prime})`


P( not an A and not an B)`=P((A cup B))^{prime}[A^{prime} cap B^{prime}=(A cup B)^{prime}]`

`
=1-{P}({A} cup {B})`

`
=1-[{P}({A})+{P}({B})-{P}({A} cap {B})]`

`
=1-[frac{1}{4}+frac{1}{2}-frac{1}{8}]`

`
=1-frac{5}{8}`

`
=frac{3}{8}`