Q79 / 160 · TS EAMCET 2024 (09 May Shift 1) · Mathematics

If the probability that a student selected at random from a particular college is good at mathematics is 0.6 , then the probability of having two students who are good at mathematics in a group of 8 students of that college standing in front of the college is

  • A
    $\frac{2^6 \times 3^2 \times 7}{5^8}$
  • B
    $\frac{2^6 \times 3^2 \times 7}{5^6}$
  • C
    $\frac{2^8 \times 3^2 \times 7}{5^6}$
  • Correct answer
    D
    $\frac{2^8 \times 3^2 \times 7}{5^8}$

Solution

$p=0.6, q=0.4, n=8$ $\begin{aligned} & P(X=2)={ }^8 C_2 \times(0.6)^2 \times(0.4)^6 \\ & =\frac{8 \times 7}{2} \times \frac{3^2}{5^2} \times \frac{2^6}{5^6}=\frac{2^8 \times 3^2 \times 7}{5^8}\end{aligned}$

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

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