(D) Given,$p = 0.001$ and $n = 2000$. Since $n$ is large and $p$ is very small,we use the Poisson distribution. The mean $\lambda = np = 2000 \times 0

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(D) Given,$p = 0.001$ and $n = 2000$. Since $n$ is large and $p$ is very small,we use the Poisson distribution. The mean $\lambda = np = 2000 \times 0.001 = 2$. The probability mass function for the Poisson distribution is given by $P(X = x) = \frac{\lambda^x e^{-\lambda}}{x!}$. For $x = 3$,we have: $P(X = 3) = \frac{2^3 e^{-2}}{3!} = \frac{8 \times e^{-2}}{6} = \frac{4}{3e^2}$. Thus,the correct option is $D$.

Class 11 Chemistry Data Entry - Chemistry Level 0 of all question bank

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 a bad reaction is:

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

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