A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a number divisible by 5.

Given:

A box contains 90 discs which are numbered from 1 to 90.

One disc is drawn at random from the box.

To do:

We have to find the probability that it bears a number divisible by 5.

Solution:

A box contains discs numbered \( 1,2,3,4, .., 89,90 \).

This implies,

The total number of possible outcomes $n=90$.

Numbers divisible by 5 from 1 to 90 are $5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90$.

Total number of favourable outcomes $=18$.

We know that,

Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

Therefore,

Probability that the disc bears a number divisible by 5 $=\frac{18}{90}$

$=\frac{1}{5}$

The probability that it bears a number divisible by 5 is $\frac{1}{5}$.