Question

If $P\left(A\right)=\frac{1}{4},P\left(B\right)=\frac{2}{5}$ and $P(A\cup B)=\frac{1}{2}$, find the value of $P(A^{\prime }\cap B^{\prime })$

Answer 1

We have,

$P\left(A\right)=\frac{1}{4}$

$P\left(B\right)=\frac{2}{5}$

$P(A\cup B)=\frac{1}{2}$

$P(A^{\prime }\cap B^{\prime })=?$

So,

We know that,

$P(A^{\prime }\cap B^{\prime })=P{(A\cup B)}^{\prime }$

$P{(A\cup B)}^{\prime }=1-P(A\cup B)$

$=1-\frac{1}{2}$

$=\frac{1}{2}$

Hence, this is the answer.