The probability that an individual suffers a bad reaction from an injection is 0.001 . The probability that…

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
  1. $\frac{1}{e^2}$
  2. $\frac{2}{3 e^2}$
  3. $\frac{8}{3 e^2}$
  4. $\frac{4}{3 e^2}$

Solution

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

Asked in: AP EAMCET 2011

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