Question

10% bulbs manufactured by a company are defective. The probability that out of a sample of 5 blubs, none is defective, is

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

Answer 1

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

Probability of defective bulb =$\frac{10}{100}=\frac{1}{10}$
Probability of non-defective blub = $1-\frac{1}{10}=\frac{9}{10}$
Probability that out of a sample of 5 bulbs, none is defective
${=}^5{C}_5{\left(\frac{9}{10}\right)}^5{\left(\frac{1}{10}\right)}^0={\left(\frac{9}{10}\right)}^5$