Question

$10\%$ bulbs manufactured by a company are found to be defective. The probability that out of a sample of $5$ bulbs none is defective is

• A. ${\left(\frac{1}{2}\right)}^5$
• B. ${\left(\frac{1}{10}\right)}^5$
• C. ${\left(\frac{9}{10}\right)}^4\left(\frac{1}{10}\right)$
• D. ${\left(\frac{9}{10}\right)}^5$

Answer 1

The correct option is D ${\left(\frac{9}{10}\right)}^5$

Probability of defective bulb
$=\frac{10}{100}=\frac{1}{10}$
So the probability of undefective bulb
$=1-\frac{1}{10}=\frac{9}{10}$
Probabilty that out of a sample of $5$ bulbs no bulb is defective $={}^5{C}_0{\left(\frac{1}{10}\right)}^0{\left(\frac{9}{10}\right)}^5={\left(\frac{9}{10}\right)}^5$