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If $A$ and $B$ are independent events such that odds in favour of $A$ is $2: 3$ and odds
against $B$ is $4: 5$, then $P(A \cap B)=$
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against $B$ is $4: 5$, then $P(A \cap B)=$
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Verified Answer
The correct answer is:
$\frac{2}{9}$
Given $P(A)=\frac{2}{5} \Rightarrow P\left(A^{\prime}\right)=\frac{3}{5}$ and $P\left(B^{\prime}\right)=\frac{4}{9} \Rightarrow P(B)=\frac{5}{9}$
Since $A$ and $B$ are independent events,
$\therefore \mathrm{P}(\mathrm{A} \cap \mathrm{B})=\mathrm{P}(\mathrm{A}) \cdot \mathrm{P}(\mathrm{B})=\frac{2}{5} \times \frac{5}{9}=\frac{2}{9}$
Since $A$ and $B$ are independent events,
$\therefore \mathrm{P}(\mathrm{A} \cap \mathrm{B})=\mathrm{P}(\mathrm{A}) \cdot \mathrm{P}(\mathrm{B})=\frac{2}{5} \times \frac{5}{9}=\frac{2}{9}$
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