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 number of discs = 90

We know that, P(E) = (Number of favorable outcomes/ Total number of outcomes)

(i) two-digit number

Since numbers from 1 to 9 are single digits, the total number of two digits is 90-9, which equals 81.

P (two-digit number) = 81/90 

= 9/10 = 0.9

(ii) perfect square numbers are 1, 4, 9, 16, 25, 36, 49, 64 and 81

Total number of perfect square numbers = 9

P ( perfect square number) = 9/90 

= 1/10 = 0.1

(iii) the number divisible by 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, and 90

So, total numbers which are divisible by 5 = 18 

P (a number divisible by 5) = 18/90 

= 1/5 = 0.2