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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) more than one(ii) at least one will fuse after 150 days of use.
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) more than one
(ii) at least one will fuse after 150 days of use.
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) more than one
(ii) at least one will fuse after 150 days of use.

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

(i) Probability of more than one such bulb in a random drawing of 5 bulbs =P(X>1)

=1-P(X \leq 1)

=1-\left[(0.95)^{4} \times 1.2\right]

(ii) Probability of at least one such bulb in a random drawing of 5 bulbs =\mathrm{P}(\mathrm{X} \geq 1)

=1-\mathrm{P}(\mathrm{X}<1)

=1-\mathrm{P}(\mathrm{X}=0)

=1-(0.95)^{5}

i

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