Q99 / 160 · TS EAMCET 2011 · Mathematics

The probability that an individual suffers a bad reaction from an injection is 0.001 . The probability that out of 2000 individuals exactly three will suffer bad reaction is

  • A
    $\frac{1}{e^2}$
  • B
    $\frac{2}{3 e^2}$
  • C
    $\frac{8}{3 e^2}$
  • Correct answer
    D
    $\frac{4}{3 e^2}$

Solution

Given, $p=0.001, n=2000$ $\therefore \quad \text { Mean }=n p=2000 \times 0.001=2$ Using poisson distribution, $\begin{aligned} & P(X=x)=\frac{\lambda^x e^{-x}}{x !} \\ \therefore \quad & P(X=3)=\frac{2^3 e^{-3}}{3 !}=\frac{4}{3 e^2} \end{aligned}$

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

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