If $\mathrm{E}$ and $\mathrm{F}$ are events such that $P(\bar{F})=0.7$ and $P(E \cap F)=0.2$, then…

If $\mathrm{E}$ and $\mathrm{F}$ are events such that $P(\bar{F})=0.7$ and $P(E \cap F)=0.2$, then $\mathrm{P}(E \mid F)$ is
  1. $2 / 3$
  2. $1 / 3$
  3. $3 / 4$
  4. $1 / 4$

Solution

$\mathrm{P}(\overline{\mathrm{F}})=0.7$ and $\mathrm{PE} \mathrm{nF})=0.2$ $P\left(\frac{E}{F}\right)=\frac{P(E n F)}{P(F)}$ Here, $\mathrm{P}(\mathrm{F})=1-\mathrm{P}(\overline{\mathrm{F}})$ $ =1-0.7=0.3 $ $ P\left(\frac{E}{F}\right)=\frac{0.2}{0.3}=\frac{2}{3} $

Asked in: AP EAMCET 2022 (06 Jul Shift 1)

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