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In a university campus, the probability that a person chosen at random is an engineering students is $\frac{1}{5}$. The probability of having atmost two engineering students in a sample of 8 people is
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Verified Answer
The correct answer is:
$19 \times \frac{4^7}{5^8}$
Given, chosen person is an engineering student having probability is $\frac{1}{5}$.
In sample of 8 student, for at most two students are engineering students there may be none of students are engineer on only one is engineer or only 2 is engineer:-
$$
\begin{aligned}
& \Rightarrow\left(\frac{4}{5}\right)^8+{ }^8 \mathrm{C}_1 \times\left(\frac{1}{5}\right)\left(\frac{4}{5}\right)^7+{ }^8 \mathrm{C}_2 \times\left(\frac{1}{5}\right)^2 \times\left(\frac{4}{5}\right)^2 \\
& \Rightarrow 19 \times \frac{4^7}{58}
\end{aligned}
$$
In sample of 8 student, for at most two students are engineering students there may be none of students are engineer on only one is engineer or only 2 is engineer:-
$$
\begin{aligned}
& \Rightarrow\left(\frac{4}{5}\right)^8+{ }^8 \mathrm{C}_1 \times\left(\frac{1}{5}\right)\left(\frac{4}{5}\right)^7+{ }^8 \mathrm{C}_2 \times\left(\frac{1}{5}\right)^2 \times\left(\frac{4}{5}\right)^2 \\
& \Rightarrow 19 \times \frac{4^7}{58}
\end{aligned}
$$
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