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 perfect square number
(iii) a number divisible by 5.
The total numbers of discs = 50
P(E) = (Number of favourable outcomes/ Total number of outcomes)
(i) Total number of discs having two digit numbers = 81
(Since 1 to 9 are single digit numbers and so, total 2 digit numbers are 90 - 9 = 81)
P (bearing a two-digit number) = 81/90
= 9/10 = 0.9
(ii) Total number of perfect square numbers = 9 (1, 4, 9, 16, 25, 36, 49, 64 and 81)
P (getting a perfect square number) = 9/90
= 1/10 = 0.1
(iii) Total numbers which are divisible by 5 = 18 (5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85 and 90)
P (getting a number divisible by 5) = 18/90
= 1/5 = 0.2