Question

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

• A. $\frac{2}{e^2}$
• B. $\frac{2}{5e^2}$
• C. $\frac{8}{5e^2}$
• D. $\frac{4}{3e^3}$

Answer 1

The correct option is D $\frac{4}{3e^3}$

Given: $p=0.001,n=2000$

$\Rightarrow$ Mean $=np=2000\times 0.001=2$

Using Poisson distribution:

$\Rightarrow P(X=x)=\frac{{\lambda }^x{e}^{-x}}{x!}$

$\Rightarrow P(X=3)=\frac{2^3{e}^{-3}}{3!}=\frac{8e^{-3}}{6}=\frac{4}{3e^3}$