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In a box containing 100 bulbs, 10 bulbs...

In a box containing 100 bulbs, 10 bulbs are defective. Probability that out of a sample of 5 bulbs, none is defective, is

A

`10^(-1)`

B

`(1/2)^(5)`

C

`(9/10)^(5)`

D

`9/10`

Text Solution

Verified by Experts

The correct Answer is:
A
Th consecutive selection of defective bulbs from a box is a Bernaulli's experiment.
Let `X` represents number of defective bulbs in a samle of 5 bulbs.
Therefore probability of getting a defective bulb
`p=10/100=1/10`
and `q=1-p=1-1/10=9/10`
Clearly `X` is a binomial distribution with `n=5, p=1/10` and `q=9/10`
`:. P(X=r)=.^(n)C_(r)p^(r)q^(n-r)=.^(5)C_(r).(1/10)^(r)(9/10)^(5-r)`
`P` (no defective bulb)
`=P(X=0)=.^(5)C_(0).(1/10)^(0)(9/10)^(5)`
`=1xx1xx(910)^(5)=(9/10)^(5)`
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