Question

A bag contains cards numbered from 5 to 100 such that each card bears a different number. A card is drawn at random. Find the probability that the number on the card is:

• [(i)] a perfect square
• [(ii)] a 2-digit number

Hint:

Count favourable outcomes and divide by total outcomes to find probability.

Answer 1

Total numbers = \(100 - 5 + 1 = 96\) (i) Perfect squares between 5 and 100 are: 9, 16, 25, 36, 49, 64, 81, 100 Count = 8 \[ P(\text{perfect square}) = \frac{8}{96} = \frac{1}{12} \] (ii) 2-digit numbers = 10 to 99 Count = \(99 - 10 + 1 = 90\) \[ P(\text{2-digit number}) = \frac{90}{96} = \frac{15}{16} \]