Question

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 (i) a two-digit number, (ii) a number divisible by 5 ?

Answer 1

Total number of the discs which are numbered from 1 to 90 = 90
∴ Total number of outcomes = 90

(i) Let A be the event that one disc drawn at random from the box bears a two-digit number.
Number of discs that bears a two-digit number = 90 − 9 = 81
Favourable number of outcomes = 81

∴ P(A) =\[\frac{\text{Favourable number of outcomes}}{\text{Total number of outcomes}} = \frac{81}{90} = \frac{9}{10}\]

(ii) Let B be the event that one disc drawn at random from the box bears a number divisible by 5.
The outcomes in favour of the event B are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85 and 90.
Favourable number of outcomes = 18

∴ P(B) =\[\frac{\text{Favourable number of outcomes}}{\text{Total number of outcomes}} = \frac{18}{90} = \frac{1}{5}\]