Question

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.

Answer 1

Hello!

• Total number of outcomes = $\bf{90}$.

(i) Two digit numbers 10 to 90 which are $\underline{\sf 81}$ in number.

Then,
P (a two-digit number) = $\dfrac{81}{90} = \red{\bf{\dfrac{9}{10}}}$

(ii) Perfect squares are $\underline{\sf 1,\:4,\:9,\:16,\:25,\:36,\:49\:63,\:81}$

Then,
P (perfect square) = $\dfrac{9}{90} = \red{\bf{\dfrac{1}{10}}}$

(iii) Numbers divisible by 5 are 5, 10 ... 90 which are $\underline{\sf 18}$ in number.

Then,
P (numbers divisible by 5) = $\dfrac{18}{90} = \red{\bf{\dfrac{1}{5}}}$

Cheers!