Choose the correct answer from the given four options. If A and B… - Vidyadip

Question

Choose the correct answer from the given four options.
If A and B are two independent events with $\text{P}(\text{A})=\frac{3}{5}$ and $\text{P}(\text{A})=\frac{4}{9},$ then $\text{P}(\text{A'}\cap\text{B'})$ equals:

$\frac{4}{15}$
$\frac{8}{45}$
$\frac{1}{3}$
$\frac{2}{9}$

✓

Answer

$\frac{2}{9}$

Solution:
Since A and B are independent events, A' And B' are aslo independent.
$\therefore\text{P}(\text{A}'\cap\text{B}')=\text{P}(\text{A})\cdot\text{P}(\text{B})$
$=\big[1-\text{P}(\text{A})\big]\big[1-\text{P}(\text{B})\big]$
$=\Big(1-\frac{3}{5}\Big)\Big(1-\frac{4}{9}\Big)$
$=\frac{2}{5}\cdot\frac{5}{9}=\frac{2}{9}$

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