In a box containing 100 bulbs, 10 are defective. If 5 bulbs are drawn one after another with replacement, then the probability that none is defective, is
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Solution
Let X : Be the number of defective bulbs
Picking bulbs is a Bernoulli trial
So, X has binomial distribution
P(X=x)=nCxqn−xpx
n= number of times we pick a bulb =5
p= probability of getting defective bulb =10100=110
q=1−p=1−110=910
Hence,
P(X=x)=5Cx(110)x(910)5−x
We need to find probability that no bulb is defective i.e