Question

A box contains 120 discs, which are numbered from 1 to 120. If one disc is drawn at random from the box, find the probability that
(i) it bears a 2-digit number
(ii) the number is a perfect square.

Answer 1

Probability: Drawing a Disc from a Box

Total number of discs in the box = 120

So, the total number of possible outcomes is: 120

(i) The disc bears a 2-digit number

The 2-digit numbers range from 10 to 99 (inclusive).
Number of 2-digit numbers = (99 − 10) + 1 = 90

Number of favorable outcomes = 90
Probability of 2-digit number: \[ \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{90}{120} = \frac{3}{4} \] \[ \text{P(2-digit number)} = \boxed{\frac{3}{4}} \]

(ii) The number is a perfect square

We list the perfect squares from 1 to 120: \[ 1^2 = 1,\quad 2^2 = 4,\quad 3^2 = 9,\quad 4^2 = 16,\quad 5^2 = 25, \\ 6^2 = 36,\quad 7^2 = 49,\quad 8^2 = 64,\quad 9^2 = 81,\quad 10^2 = 100 \] \(11^2 = 121\) is more than 120, so we stop at 100.

Number of perfect squares = 10
Probability of perfect square: \[ \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{10}{120} = \frac{1}{12} \] \[ \text{P(perfect square)} = \boxed{\frac{1}{12}} \]