Question

A manufactured product on an average has $2$ defects per unit of product produced. If the number of defects follows P.D., the probability of finding zero defects is

• A. $e^{-2}$
• B. $1-e^{-2}$
• C. $\frac{e^{-2}{2}^1}{\angle 1}$
• D. $e^{-002}$

Answer 1

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

By using Poisson distribution,
$P(x;\mu )=\frac{e^{-\mu }{\mu }^x}{x!}$
: 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; ): The Poisson probability that exactly x successes occur in a Poisson experiment, when the mean number of successes is
$\mu =2$ (defects per unit of product produced)
x = 0 (zero defects)
$P(0;2)=\frac{e^{-2}{2}^0}{0!}=e^{-2}$