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(i) none(ii) not more than one

Home » 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(i) none(ii) not more than one

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
(i) none
(ii) not more than one

CBSE | Maths | NCERT | Probability

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
(i) none
(ii) not more than one

Solution:

Assume that in a five-trial experiment, the number of bulbs that will fuse after 150 days is $x$ .

The trials will be Bernoulli trials, as we can see, because they are made with replacement.

The fact that, as stated in the question, $\mathrm{p}=0.05$

Thus, $q=1-p=1-0.05=0.95$

Here, we can clearly observe that $x$ has a binomial representation with $n=5$ and $p=$

$0.05$

Thus, $\mathrm{P}(\mathrm{X}=\mathrm{x})={ }^{\mathrm{n}} \mathrm{C}_{\mathrm{x}} \mathrm{q}^{n-\mathrm{x}} \mathrm{p}^{\mathrm{x}}$ , where $\mathrm{x}=0,1,2 \ldots \mathrm{n}$