#### 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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#### APPEARS IN

Solution 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. Concept: Random Variables and Its Probability Distributions.