A box contains $90$ discs which are numbered $1$ to $90$. If one disc is drawn at random from the box, find the probability that it bears a:
(i) $2$-digit number less than $40$.
(ii) number divisible

Question

A box contains $90$ discs which are numbered $1$ to $90$. If one disc is drawn at random from the box, find the probability that it bears a:
(i) $2$-digit number less than $40$.
(ii) number divisible by $5$ and greater than $50$.
(iii) a perfect square number.

Accepted Answer

Step 1: Total outcomes $= 90$. (i) $2$-digit numbers less than $40$: $10$ to $39 = 30$. $P = \frac{30}{90} = \frac{1}{3}$
Step 2: (ii) Divisible by $5$ and $> 50$: $55, 60, 65, 70, 75, 80, 85, 90 = 8$. $P = \frac{8}{90} = \frac{4}{45}$
Step 3: (iii) Perfect squares: $1, 4, 9, 16, 25, 36, 49, 64, 81 = 9$. $P = \frac{9}{90} = \frac{1}{10}$

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