Choose the correct answer from the given four options. P ( B A ) … - Vidyadip

Question

Choose the correct answer from the given four options.
$\text{P}\Big(\frac{\text{B}}{\text{A}}\Big)$ is equal to:

$\frac{1}{5}$
$\frac{3}{10}$
$\frac{1}{2}$
$\frac{3}{5}$

✓

Answer

$\frac{3}{5}$

Solution:

$\text{P}\Big(\frac{\text{B}}{\text{A}'}\Big)=\frac{\text{P}(\text{B}\cap\text{A}')}{\text{P}(\text{A}')}$

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

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

$=\frac{6}{10}=\frac{3}{5}$

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