Question

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

Options

• `10^-1`

• `(1/2)^5`

• `(9/10)^5`

• `9/10`

Answer 1

`(9/10)^5`

Explanation:

Number of bulbs in the box = 100

Number of defective bulbs = 10

Probability of occurrence of a good bulb = `10/100 = 1/10`

⇒ Probability of occurrence of a good bulb = `1 - 1/10 = 9/10`

In a sample of 5 bulbs, the distribution of defective bulbs = `(9/10 + 1/10)^5`

Probability that no. bulb is defective in this sample = `(9/10)^5`