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# In a Box Containing 100 Bulbs, 10 Are Defective. What is the Probability that Out of a Sample of 5 Bulbs, None is Defective? - Mathematics

ConceptBernoulli Trials and Binomial Distribution

#### 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?

•  $\left( \frac{9}{10} \right)^5$

•  $\frac{9}{10}$

•  10−5

•  $\left( \frac{1}{2} \right)^2$

#### Solution

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

Let X denote the number of defective bulbs.
Hence, the binomial distribution is given by

$n = 5 , p = \frac{10}{100} = \frac{1}{10}$
&  $q = \frac{90}{100} = \frac{9}{10}$
$\text{ Hence, the distribution is given by }$
$P(X = r) = ^{5}{}{C}_r \left( \frac{1}{10} \right)^r \left( \frac{9}{10} \right)^{5 - r}$
$\therefore P(X = 0) = \left( \frac{9}{10} \right)^5$

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Solution In a Box Containing 100 Bulbs, 10 Are Defective. What is the Probability that Out of a Sample of 5 Bulbs, None is Defective? Concept: Bernoulli Trials and Binomial Distribution.
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