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
Total number of discs = 90
(i) Total number of two-digit numbers between 1 and 90 = 81
P (getting a two-digit number)
= 
= 
= 
(ii) Perfect squares between 1 and 90 are 1, 4, 9, 16, 25, 36, 49, 64, and 81. Therefore, total number of perfect squares between 1 and 90 is 9.
P (getting a perfect square)
= 
= 
= 
(iii) Numbers that are between 1 and 90 and divisible by 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, and 90. Therefore, total numbers divisible by 5 = 18
Probability of getting a number divisible by 5 = 
= 
23