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Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability1 Mark
Question
Given that E and F are events such that $\text{P}(\text{E})=0.6,\ \text{P}(\text{F})=0.3\ \text{and}\ \text{P}(\text{E}\cap\text{F})=0.02,\ \text{find}\ \text{P}(\text{E}|\text{F})\ \text{and}\ \text{P}(\text{F}|\text{E}) .$
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Answer

$\text{Given:}\ \ \text{P}\left(\text {E}\right)=0.6,\ \text{P}\left(\text{F}\right)=0.3\ \text{and P}\left(\text{E}\cap\text{F}\right)=0.2$
$\therefore\ \ \ \ \ \ \text{P}\left(\text{E|F}\right)=\frac {\text{P}\left(\text{E} \cap\text{F}\right)}{\text{P}\left(\text{F}\right)}=\frac{0.2}{0.3}=\frac{2}{3}$
$\text{And}\ \ \ \text{P}\left(\text{F}|\text {E}\right)=\frac{\text{P}\left(\text{E}\cap\text{F}\right)}{\text{P}\left(\text{E}\right)}=\frac{0.2}{0.6}=\frac{1}{3}$

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