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If $P(A)=\frac{3}{5}$ and $P(B)=\frac{1}{5}$, find $P(A \cap B)$ if $A$ and $B$ are independent events.
Solution:
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Verified Answer
$\mathrm{A}$ and $\mathrm{B}$ are independent if $\mathrm{P}(\mathrm{A} \cap \mathrm{B})$
$$
=\mathrm{P}(\mathrm{A}) \times \mathrm{P}(\mathrm{B})=\frac{3}{5} \times \frac{1}{5}=\frac{3}{25}
$$
$$
=\mathrm{P}(\mathrm{A}) \times \mathrm{P}(\mathrm{B})=\frac{3}{5} \times \frac{1}{5}=\frac{3}{25}
$$
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