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 numbes, (iii) a number divisible by 5.

Answer

` (i) 9/10 (ii) 1/10 (iii) 1/5`

Explanation

Total number of discs = 90.
(i) Number of discs bearing 2-digit numbers
= number of numbers from 10 to 90 = (90-9) = 81.
P(getting a 2-digit number) = ` 81/90 = 9/10`.
(ii) Perfect square numbers are `1^(2) , 2^(2),3^(2) , …, 9^(2)`. Their number is 9 .
Number of discs bearing perfect square numbers = 9.
` :. ` P(getting a perfect square number ) ` 9/90 = 1/10`.
(iii) Number divisible by 5 are 5,10,15, ... 90. They are 18 in number.
` :. ` P(getting a number divisible by 5) ` = 18/90 = 1/5`.