AP EAMCET · Maths · Probability
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 \(\frac{8}{3 e^2}\)
- D \(\frac{4}{3 e^2}\)
Answer & Solution
Correct Answer
(D) \(\frac{4}{3 e^2}\)
Step-by-step Solution
Detailed explanation
Given, \(p=0.001, n=2000\) \(\therefore \quad \text { Mean }=n p=2000 \times 0.001=2\) Using poisson distribution, \(\begin{aligned} & P(X=x)=\frac{\lambda^x e^{-x}}{x !} \\ \therefore \quad & P(X=3)=\frac{2^3 e^{-3}}{3 !}=\frac{4}{3 e^2} \end{aligned}\)
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