"Let $\mathrm{A}$ and $\mathrm{B}$ be two events such that $P(B \mid A)=\frac{2}{5}, P(A \mid B)=\frac{1}{7}$ and $P(A \cap B)=\frac{1}{9} \cdot$ Consider (S1) $P\left(A^{\prime} \cup B\right)=\frac{5}{6}$, (S2) $P\left(A^{\prime} \cap B^{\prime}\right)=\frac{1}{18}$ Then :"

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Accepted Answer

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$P(A/B) = {1 \over 7} \Rightarrow {{P(A \cap B)} \over {P(B)}} = {1 \over 7}$

$\Rightarrow P(B) = {7 \over 9}$

$P(B/A) = {2 \over 5} \Rightarrow {{P(A \cap B)} \over {P(A)}} = {2 \over 5}$

$P(A) = {5 \over 2}\,.\,{1 \over 9} = {5 \over {18}}$

$S2:P(A' \cap B') = {1 \over {18}}$

$S1:$ and $P(A' \cup B) = {1 \over 9} + {6 \over 9} + {1 \over {18}} = {5 \over 6}.$

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Let $\mathrm{A}$ and $\mathrm{B}$ be two events such that $P(B \mid A)=\frac{2}{5}, P(A \mid B)=\frac{1}{7}$ and $P(A \cap B)=\frac{1}{9} \cdot$ Consider

(S1) $P\left(A^{\prime} \cup B\right)=\frac{5}{6}$,

(S2) $P\left(A^{\prime} \cap B^{\prime}\right)=\frac{1}{18}$

Then :

Solution

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Let $\mathrm{A}$ and $\mathrm{B}$ be two events such that $P(B \mid A)=\frac{2}{5}, P(A \mid B)=\frac{1}{7}$ and $P(A \cap B)=\frac{1}{9} \cdot$ Consider (S1) $P\left(A^{\prime} \cup B\right)=\frac{5}{6}$, (S2) $P\left(A^{\prime} \cap B^{\prime}\right)=\frac{1}{18}$ Then :

Solution

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More Probability questions

Drill 25 more like these. Every day. Free.

Let $\mathrm{A}$ and $\mathrm{B}$ be two events such that $P(B \mid A)=\frac{2}{5}, P(A \mid B)=\frac{1}{7}$ and $P(A \cap B)=\frac{1}{9} \cdot$ Consider

(S1) $P\left(A^{\prime} \cup B\right)=\frac{5}{6}$,

(S2) $P\left(A^{\prime} \cap B^{\prime}\right)=\frac{1}{18}$

Then :