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
\[n = 5 , p = \frac{10}{100} = \frac{1}{10}\]
& \[ q = \frac{90}{100} = \frac{9}{10}\]
\[\text{ Hence, the distribution is given by } \]
\[P(X = r) = ^{5}{}{C}_r \left( \frac{1}{10} \right)^r \left( \frac{9}{10} \right)^{5 - r} \]
\[ \therefore P(X = 0) = \left( \frac{9}{10} \right)^5\]
Is there an error in this question or solution?
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.
