Question

If $A$ and $B$ are independent event such that $P\left(A\right)=\frac{3}{10},P\left(B\right)=\frac{2}{5}$, then find (i) $P\left(AandB\right)$ and (ii) $P\left(AorB\right)$

Answer 1

Given that, $A$ and $B$ are the independent event

And $P\left(A\right)=\frac{3}{10}$ and $P\left(B\right)=\frac{2}{5}$

Find

Part $\left(i\right).$ $P\left(AandB\right)$

We know that,

$P\left(AandB\right)=P\left(A\right)\times P\left(B\right)$

$=\frac{3}{10}\times \frac{2}{5}=\frac{6}{50}=0.12$

Part $\left(ii\right)$. $P\left(AorB\right)$

We know that,

$P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P\left(AandB\right)$

$=\frac{3}{10}+\frac{2}{5}-\frac{6}{50}$

$=\frac{3\times 5+2\times 10-6\times 1}{50}$

$=\frac{15+20-6}{50}$

$=\frac{29}{50}$

Hence, this is the answer.