Question

A box contains $100$ bulbs, out of which $10$ are defective. A sample of $5$ bulbs is drawn. The probability that none is defective is

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

Answer 1

Answer: (D)

Let probability of defective bulb,
$p=\frac{10}{100}=\frac{1}{10}=0.1$
and probability of non-defective bulb,
$q=1-0.1=0.9$
Here, $n=5$
$\therefore P$ [none is defective] $=P(X=0)$
$={ }^{5} C_{0}(0.1)^{0}(0.9)^{5}=1 \times(0.9)^{5}=\left(\frac{9}{10}\right)^{5}$