Question

A school purchased $50$ computers for computer lab out of which $2$ are defective. If two computers are randomly selected for inspection. What is the probability that both the computers are defective if replacement is allowed?

• A. $\frac{1}{625}$
• B. ${\left(\frac{4}{50}\right)}^2$
• C. $0.0016$
• D. $0.0064$

Answer 1

Answer: (A), (C)

$0.0016$

Given:
Number of computers purchased $=50$

Number of defective bulbs $=2$

Probability of choosing first defective computer is $\text{P(A)}=\frac{2}{50}=\frac{1}{25}$

Probability of choosing second defective computer with replacement is $\text{P(B)}=\frac{2}{50}=\frac{1}{25}$

Probablity of choosing 2 defective computers at random with replacement is $\text{P(A and B)}=\text{P(E)}=\text{P(A)}\times \text{P(B)}$

$\Rightarrow \text{P(E)}=\frac{1}{25}\times \frac{1}{25}=\frac{1}{625}=\mathrm{0.0016.}$