Q. 14

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

A. 10^{–1}

B.

C.

D.

Answer :

In this question, let us assume X represent the number of times selecting defected bulbs in a random sample of given 5 bulbs

Also, the repeated selection of defective bulbs from a box are the Bernoulli trials

Clearly, we have X has the binomial distribution where n = 5 and

And,

∴

_{Hence, probability that none bulb is defective = P (X = 0)}

∴ option C is correct

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A box has 100 pens of which 10 are defective. What is the probability that out of a sample of 5 pens drawn one by one with replacement at most one is defective?

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