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TS EAMCET · Maths · Probability

If the probability that an individual will suffer a reaction from an injection of a drug is 0.001 , then the probability that out of 2000 individuals having that injection, more than 2 individuals will suffer a reaction, is

  1. A \(\frac{5}{e^2}\)
  2. B \(1-\frac{5}{e^2}\)
  3. C \(1-\frac{4}{e^2}\)
  4. D \(\frac{4}{e^2}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(1-\frac{5}{e^2}\)

Step-by-step Solution

Detailed explanation

Here, \(n=2000, P=0.001, \lambda=n p=2\) \(\begin{aligned} P(X>2) & =1-[P(X=0)+P(X=1)+P(X=2)] \\ & =1-\left[\frac{2^0 e^{-2}}{0 !}+\frac{2^1 e^{-2}}{1 !}+\frac{2^2 e^{-2}}{2 !}\right] \\ & =1-\left[e^{-2}+2 e^{-2}+2 e^{-2}\right]=1-5 e^{-2}=1-\frac{5}{e^2} \end{aligned}\)