Q80 / 160 · TS EAMCET 2022 (19 Jul Shift 2) · Mathematics

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

  • A
    $45 \times \frac{4^6}{5^8}$
  • B
    $17 \times \frac{4^7}{5^8}$
  • C
    $27 \times \frac{4^6}{5^8}$
  • Correct answer
    D
    $19 \times \frac{4^7}{5^8}$

Solution

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:- $$ \begin{aligned} & \Rightarrow\left(\frac{4}{5}\right)^8+{ }^8 \mathrm{C}_1 \times\left(\frac{1}{5}\right)\left(\frac{4}{5}\right)^7+{ }^8 \mathrm{C}_2 \times\left(\frac{1}{5}\right)^2 \times\left(\frac{4}{5}\right)^2 \\ & \Rightarrow 19 \times \frac{4^7}{58} \end{aligned} $$

Hence, the correct answer is option: 'D'.

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