Question

The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs at least one will fuse after 150 days of use 

Answer 1

Let X be the number of bulbs that fuse after 150 days.
X follows a binomial distribution with n = 5,

\[p = 0 . 05 \text{ and }  q = 0 . 95\]

\[\text{ Or } p = \frac{1}{20}\text{ and } q = \frac{19}{20}\]

\[P(X = r) = ^{5}{}{C}_r \left( \frac{1}{20} \right)^r \left( \frac{19}{20} \right)^{5 - r} \]

\[ \text{ Probability } \left( \text{ at least one will fuse after 150 days of use } \right) = P(X \geq 1)\]
\[ = 1 - P(X = 0) \]
\[ = 1 - \left( \frac{19}{20} \right)^5 \left\{ \because P(X = 0 = \left( \frac{19}{20} \right)^5 \right\}\]