Question

In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is

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

Answer 1

Answer: (C)

$(\frac{1}{2})^5$

Answer 2

The correct option is(C): $(\frac{1}{2})^5$

The repeated selections of defective bulbs from a box are Bernoulli trials. Let X denote the number of defective bulbs out of a sample of 5 bulbs.

Probability of getting a defective bulb, p =$\frac{10}{100}=\frac{1}{10 }$

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

Clearly, X has a binomial distribution with n = 5 and $p=\frac{1}{10}$
P (none of the bulbs is defective) = P(X = 0)

=$^5C_0.(\frac{9}{10})^5$

$1.(\frac{9}{10})^5$

$(\frac{9}{10})^5$
Therefore,option (C) is correct.