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?

Options

•  \[\left( \frac{9}{10} \right)^5\] 

•  \[\frac{9}{10}\]

   

•  10⁻⁵

•  \[\left( \frac{1}{2} \right)^2\]

   

Answer 1

 \[\left( \frac{9}{10} \right)^5\]  

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

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