Choose the correct answer from the given four options.
Two events E and F are independent. If $\text{P}(\text{E})=0.3,\text{P}(\text{E}\cup\text{F})=0.5,$ then $\text{P}\Big(\frac{\text{E}}{\text{F}}\Big)-\text{P}\Big(\frac{\text{F}}{\text{E}}\Big)$ equal:
A$\frac{2}{7}$
B$\frac{3}{35}$
C$\frac{1}{70}$
D$\frac{1}{7}$
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C$\frac{1}{70}$
We have, $\text{P}(\text{E})=0.3,\text{P}(\text{E}\cup\text{F})=0.5$
Also E and F are independent.
Now $\text{P}(\text{E}\cup\text{F})=\text{P}(\text{E})+\text{P}(\text{F})-\text{P}(\text{E}\cap\text{F})$
$\Rightarrow0.5=0.3+\text{P}(\text{F})-0.3\text{P}(\text{F})$
$\Rightarrow\text{P}(\text{F})=\frac{0.5-0.3}{0.7}=\frac{2}{7}$
$\therefore\text{P}\Big(\frac{\text{E}}{\text{F}}\Big)-\text{P}\Big(\frac{\text{F}}{\text{E}}\Big)$
$=\text{P}(\text{E})-\text{P}(\text{F})$ (as E and F are indepandent)
$=\frac{3}{10}-\frac{2}{7}=\frac{1}{70}$
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Choose the correct answer from the given four options.
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