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
(a)A two-digit number (b) a number divisible by 5
Total no. of possible outcomes = 90 {1, 2, 3, … 90}
(i) E ⟶ event of getting 2 digit no.
No. of favourable outcomes = 81 {10, 11, 12, …. 90}
Probability P(E) = (No.of favorable outcomes)/(Total no.of possible outcomes)
P(E) = 81/90 = 9/10
(ii) E ⟶ event of getting a perfect square.
No. of favourable outcomes = 9 {1, 4, 9, 16, 25, 26, 49, 64, 81}
P(E) = 9/90=1/10
(iii) E ⟶ event of getting a no. divisible by 5.
No. of favourable outcomes = 18 {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90}
P(E) = 18/90 = 1/5
Total number of discs in the box = 90
(a) Two digit numbers from 1 to 90 = 81
P(getting a two-digit number) = 81/90 = 9/10
(b) Numbers divisible by 5 from 1 to 90 = 5, 10, …. , 90,
Total numbers = 18
P(getting a number which is divisible by 5) = 18/90 = 1/5