Question

The probability that a bulb produced by a factory will fuse after 150 days of used is 0.05. Find the probability that out of 5 such bulbs
(iv) atleast one will fuse after 150 days of use

Answer 1

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

p=P(success) = 0.05 and q = 1-p=1-0.05 = 0.95

X has a binomial distrubtion with n= 5, p=0.05 and q=0.95

P(X=r) = ${}^5{C}_r.\left(0.05{)}^r\right(0.95{)}^{5-r}$
(iv) Required probability = P(atleast one) = $=P(X\ge 1)=1-P\left(0\right)=1-(0.95{)}^5$