Question

The probability that a certain kind of component will survive a given shock test is $3/4$. Find the probability that among $5$ components tested exactly $2$ will survive.

• A. $\frac{90}{124}$
• B. $\frac{9}{14}$
• C. $\frac{90}{1024}$
• D. None of these

Answer 1

Answer: (C)

$\frac{90}{1024}$

Component will survive the test = $\frac{3}{4}$

Component will not survive the test = $\frac{1}{4}$

2 survive the test = $(\frac{3}{4}{)}^2\times (\frac{1}{4}{)}^3\times \frac{5!}{3!\times 2!}=\frac{90}{1024}$