Question

Cards marked with all 2-digit numbers are placed in a box and are mixed thoroughly. One card is drawn at random. Find the probability that the number on the card is

(a) divisible by 10
(b) a perfect square
(c) a prime number less than 25

Answer 1

Cards are marked with numbers 10, 11, 12, …, 99.
Total number of cards = 90

(a) The number of cards divisible by 10 are 10, 20, 30, 40, 50, 60, 70, 80, 90.
The number of favourable cases = 9
Probability of getting a card with a number divisible by 10 = $\frac{9}{90}=\frac{1}{10}$

(b) The numbers of cards which are perfect squares are 16, 25, 36, 49, 64, 81
The number of favourable cases = 6
Probability of getting a card that is a perfect square = $\frac{6}{90}=\frac{1}{15}$

(c) Prime numbers less than 25 are 2, 3, 5, 7, 11 , 13, 17, 19, 23.
The number of favourable cases = 9
Probability of getting a card with a prime number less than 25 = $\frac{9}{90}=\frac{1}{10}$