Question

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

(i) none

(ii) not more than one

(iii) more than one

(iv) at least one

will fuse after 150 days of use.

Answer 1

Let X represent the number of bulbs that will fuse after 150 days of use in an experiment of 5 trials. The trials are Bernoulli trials.

It is given that, p = 0.05

X has a binomial distribution with n = 5 and p = 0.05

(i) P (none) = P(X = 0)

(ii) P (not more than one) = P(X ≤ 1)

(iii) P (more than 1) = P(X > 1)

(iv) P (at least one) = P(X ≥ 1)