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Question
From a lot of 25 bulbs of which 5 are defective a sample of 5 bulbs was drawn at random with replacement. Find the probability that the sample will contain -
(a) exactly 1 defective bulb.
(b) at least 1 defective bulb.
Solution
Let X be the number of defective items.
P(an item is defective)=p=5/25=0.2, q=0.8, n=5
a) P(exactly one defective bulb)
`=P(X=1)`
`=""^5C_1(p)^1q^5`
=(5)(0.2)(0.8)4
=0.4096
b)P(atleastone defective bulb)
`=1-P(X=0)`
`=1-""^5C_0(0.2)^0(0.8)^5`
=1-(1)(1)(0.3277)
=0.6723
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