Question

10% of tools produced by a certain manufacturing process turn out to be defective. Assuming binomial distribution, the probability of 2 defective in simple of 10 tools chosen at random, is

• A. 0.368
• B. 0.194
• C. 0.271
• D. None of these

Answer 1

The correct option is B 0.194

Let the event of a tool being defective be $X$.

$\therefore$ Probability of $X$ occurring = $p=\frac{1}{10}$

$\therefore q=1-p=\frac{9}{10}$

Now, as the process follows the binomial distribution, the probability of 2 tools being defective is

${}^{10}{C}_2{p}^2{q}^{10-2}$

$={}^{10}{C}_2{p}^2{q}^8$

$=\frac{10!}{2!8!}{\left(\frac{1}{10}\right)}^2{\left(\frac{9}{10}\right)}^8$

$=0.194$

This is the required solution.