Question

A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears a prime number less than 23, is ______.

Options

• `7/90`

• `9/90`

• `1/9`

• `10/90`

• `4/15`

• `4/45`

• `8/89`

• \[\frac{9}{89}\]

Answer 1

A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears a prime number less than 23, is `underlinebb(4/45)`.

Explanation:

There are 90 discs numbered from 1 to 90.

∴ Total number of outcomes = 90

The prime numbers less than 23 are 2, 3, 5, 7, 11, 13, 17 and 19.

So, the favourable number of outcomes are 8.

∴ P(disc drawn bears a prime number less than 23) = \[\frac{\text{ Favourable number of outcomes }}{\text{ Total number of outcomes }} = \frac{8}{90} = \frac{4}{45}\]