Question

$Evaluate \ P(A∩B)\ if \ 2P(A) = P(B) =$ $\frac {5}{13}$ $and \ P(A|B)=$ $\frac 25$

Answer 1

$Given:$
$2P(A) = P(B) =$ $\frac {5}{13}$,

$P(A|B)=\frac 25$

$∴P(A)=\frac {5}{26}$

$Now,$ $P(A∩B)=P(B|A).P(B)$

$P(A∩B)=\frac 25\times\frac {5}{13}$

$P(A∩B) =\frac {2}{13}$

$Now,$ $P(A∪B)=P(A)+P(B)-P(A∩B)$

$P(A∪B) =\frac {5}{26}+\frac {5}{13}-\frac {2}{13}$

$P(A∪B) =\frac {11}{26}$