Question

A box contains 90 discs which are numbered from 1 to 90. If one discs 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.

Answer 1

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