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.

Answer 1

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