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If is observed that $25 \%$ of the cases related to child labour reported to the police station are solved. If 6 new cases are reported, then the probability that at least 5 of them will be solved is
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Verified Answer
The correct answer is:
$\frac{19}{4096}$
We have probability of cases getting solved $=25 \%=\frac{1}{4}$
$\mathrm{p}=\frac{1}{4} \Rightarrow \mathrm{q}=\frac{3}{4}$ and we have $\mathrm{n}=6, \mathrm{x}=5,6$
Hence required probability
$$
\begin{aligned}
& =\left[{ }^6 \mathrm{C}_5\left(\frac{1}{4}\right)^5\left(\frac{3}{4}\right)^1\right]+\left[{ }^6 \mathrm{C}_6\left(\frac{1}{4}\right)^6\left(\frac{3}{4}\right)^0\right] \\
& =\frac{(6)(3)}{(4)^6}+\frac{1}{(4)^6}=\frac{19}{(4)^6}=\frac{19}{4096}
\end{aligned}
$$
$\mathrm{p}=\frac{1}{4} \Rightarrow \mathrm{q}=\frac{3}{4}$ and we have $\mathrm{n}=6, \mathrm{x}=5,6$
Hence required probability
$$
\begin{aligned}
& =\left[{ }^6 \mathrm{C}_5\left(\frac{1}{4}\right)^5\left(\frac{3}{4}\right)^1\right]+\left[{ }^6 \mathrm{C}_6\left(\frac{1}{4}\right)^6\left(\frac{3}{4}\right)^0\right] \\
& =\frac{(6)(3)}{(4)^6}+\frac{1}{(4)^6}=\frac{19}{(4)^6}=\frac{19}{4096}
\end{aligned}
$$
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