Question

The probability that a bulb produced by a factory will fuse after $100$ days of use is $0.05$. Find the probability that out of $5$ such bulbs at least one will fuse after $100$ days of use.

Answer 1

mean = np=$100\times$ 0.05=5=m.

Exponential distribution p(x=x)=$\frac{e^{-m}{m}^x}{x!}$

$P(x\ge 1)=1-p(x\le )$

$=1-p(x=0)$

$=1-\frac{e^{-5}{.5}^0}{0!}$

$=1-e^{-5}$

=0.9932