Question

The probability of a resistor being defective is 0.02. There are 50 such aresistors in a circuit. The probability of two or more defective resistors in the circuit (round off to two decimal places) is .

• A. 0.26

Answer 1

The correct option is A 0.26
Probabbility of a resistor being defective

p(def) = 0.02

Numbers of resistors = 50

Approximated Poisson distribution will have mean $=\mu =np$

$\Rightarrow \mu =50\times 0.02=1$

Poisson distribution,

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

$\text{p(0 defective)}=\frac{e^{-\mu }{\mu }^0}{0!}=e^{-1}$

$\text{p(1 defective)}=\frac{e^{-\mu }{\mu }^1}{1!}=e^{-1}$

p(2 or more defective) = 1 - p(0 defective) - p(1 defective)

$\Rightarrow$ p(2 or more defective)

$=1-e^{-1}-e^{-1}=1-2e^{-1}$

= 0.26