Question

If $3$ of electric bulbs manufactured by a company are defective; the probability that in a sample of $100$ bulbs exactly five are defective is

• A. $\frac{e^{-0.03}(0.03{)}^5}{5!}$
• B. $\frac{e^{-0.3}{0.03}^5}{5!}$
• C. $\frac{e^{-3}{0.03}^5}{5!}$
• D. $\frac{e^{-0.3}{3}^{-5}}{5!}$

Answer 1

The correct option is A $\frac{e^{-0.03}(0.03{)}^5}{5!}$

Poisson probability formula:

$p(x,\mu )=\frac{\left(e^{-\mu }\right)\left({\mu }^x\right)}{x!}$

$x\to$ actual number of occuring successes

$\mu \to$ average of the number of successes within a specified region

No. of electric bulbs defective in a sample$=3$

Here, success is selecting a defective bulb

Average of the number of defective electric bulbs in a sample$=\frac{3}{100}=0.03$

$\mu =0.03$

Probability of selecting exactly $5$ defective bulbs $(x=5)$

i.e., $P(5,0.03)=\frac{e^{-0.03}(0.03{)}^5}{5!}$.