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Solve the following.
The probability that a bulb produced in a factory will fuse after 150 days of use is . Find the…
The probability that a bulb produced in a factory will fuse after 150 days of use is $0.05$. Find the probability that out of 5 such bulbs:
Not more than one will fuse after 150 days of use.
Answer
Answer
AI$X$ = number of bulbs that fuse, binomial with $n = 5$, $p = 0.05$, $q = 0.95$.
$P(X \le 1) = P(X = 0) + P(X = 1) = (0.95)^5 + 5(0.05)(0.95)^4$
$= 0.7738 + 0.2036 = 0.9774$
Final answer: $0.9774$
From ISC 2020 Mathematics Paper 1, question 14(ii).