Question

The incidence of an occupational disease to the workers of a factory is found to be $\frac{1}{5000}$ . If there are $10,000$ workers in a factory then the probability that none of them will get the disease is

• A. $e^{-1}$
• B. $e^{-2}$
• C. $e^3$
• D. $e^4$

Answer 1

The correct option is B $e^{-2}$

By using Poisson distribution,

$P(x;\mu )=\frac{e^{-\mu }{\mu }^x}{x!}$

$\mu$: The mean number of successes that occur in a specified region.

$x:$ The actual number of successes that occur in a specified region.

$P(x;$$\mu$ ): The Poisson probability that exactly x successes occur in a Poisson experiment, when the mean number of successes is $\mu$

$\mu =10000\times \frac{1}{5000}=2$

$x=0$

$P(0;2)=\frac{e^{-2}{2}^0}{0!}=e^{-2}$