Question

In a box containing $100$ bulbs, $10$ are defective. What is the probability that out of a sample of $5$ bulbs, none is defective ?

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

Answer 1

Answer: (C)

${\left(9/10\right)}^5$

Probability for a defective bulb $=\frac{10}{100}=\frac{1}{10}$
$\therefore$ probability for a non-defective bulb $=1-\frac{1}{10}=\frac{9}{10}$
$\therefore$ Required probability $=\frac{9}{10}\times \frac{9}{10}\times \frac{9}{10}\times \frac{9}{10}\times \frac{9}{10}={\left(\frac{9}{10}\right)}^5$