Question

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 1

It is given that 10 bulbs from 100 are defective.

Let the number of defective bulbs from a sample space of 5 bulbs is represented by X.

The probability of getting a defective bulb is,

p= 10 100 = 1 10

So,

q=1−p =1− 1 10 = 9 10

Then X has a binomial distribution with n=5 and p= 1 10 .

The probability of x successes P( X=x ) is,

P( X=x )= C n x q n−x p x = C 5 x ( 9 10 ) 5−x ( 1 10 ) x

Where, x=0,1,…,n.

The probability of getting 0 defective bulbs is,

P( X=0 )= C 5 0 ( 9 10 ) 5 ( 1 10 ) 0 =1⋅ 9 5 10 5 ( 1 ) = ( 9 10 ) 5

Therefore, option (C) is correct.