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If $\mathrm{A}$ and $\mathrm{B}$ are two independent events and $\mathrm{P}(\mathrm{A})=\frac{3}{5}, \mathrm{P}(\mathrm{B})=\frac{2}{3}$, then $\mathrm{P}\left(\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}\right)=$
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The correct answer is:
$\frac{2}{15}$
$\mathrm{P}(\mathrm{A})=\frac{2}{3} \Rightarrow \mathrm{P}\left(\mathrm{A}^{\prime}\right)=1-\mathrm{P}(\mathrm{A})=1-\frac{2}{3}=\frac{1}{3}$
$\therefore \mathrm{P}\left(\mathrm{A}^{\prime} \cap \mathrm{B}\right)=\mathrm{P}\left(\mathrm{A}^{\prime}\right) \cdot \mathrm{P}(\mathrm{B})$
$=\frac{1}{3} \times \frac{3}{5}=\frac{1}{5}$
$\therefore \mathrm{P}\left(\mathrm{A}^{\prime} \cap \mathrm{B}\right)=\mathrm{P}\left(\mathrm{A}^{\prime}\right) \cdot \mathrm{P}(\mathrm{B})$
$=\frac{1}{3} \times \frac{3}{5}=\frac{1}{5}$
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