Q57 / 150 · MHT CET 2022 (05 Aug Shift 1) · Mathematics

It is observed that $30 \%$ of the students appearing for a certain entrance test are science students. If 5 students are randomly selected from this group,the probability of having 2 science students among these students is

  • Correct answer
    A
    $0.3087$
  • B
    $0.2547$
  • C
    $0.1087$
  • D
    $0.3437$

Solution

The required probability $={ }^5 C_2\left(\frac{30}{100}\right)^2 \times\left(\frac{70}{100}\right)^3$ $\begin{aligned} & =10 \times \frac{3}{10} \times \frac{3}{10} \times \frac{7}{10} \times \frac{7}{10} \times \frac{7}{10} \\ & =\frac{3087}{10000}=0.3087\end{aligned}$

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

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