Question

If $P\left(A\right)=\frac{1}{2},P\left(B\right)=\frac{7}{12}$ and P (not A not B)$=\frac{1}{4}$. State whether A and B are independent.

Answer 1

$P\left(A\right)=\frac{1}{2};P\left(B\right)=\frac{7}{12}$

P(met A or not B) $=P\left(A^{\prime }or{B}^{\prime }\right)$

$\frac{1}{4}=P(A^{\prime }\cup B^{\prime })$

$\frac{1}{4}=P(A\cap B{)}^{\prime }$

$\frac{1}{4}=1-P(A\cap B)$

$P(A\cap B)=1-\frac{1}{4}$

$=\frac{3}{4}$