Question

Cards numbered 1 to 30 are put in a bag. A card is drawn at random from this bag. Find the probability that the number on the drawn card is

(i) not divisible by 3
(ii) a prime number greater than 7
(iii) not a perfect square number [CBSE 2014]

Answer 1

Total number of outcomes = 30

(i) There are 10 numbers divisible by 3.

∴ Number of numbers not divisible by 3 = 30 − 10 = 20

So, the favourable number of outcomes are 20.

∴ P(drawing a card with number not divisible by 3) = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{20}{30}=\frac{2}{3}$

(ii) Prime numbers greater than 7 are 11, 13, 17, 19, 23 and 29.

So, the favourable number of outcomes are 6.

∴ P(drawing a card with prime number greater than 7) = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{6}{30}=\frac{1}{5}$

(iii) The perfect squares are 1, 4, 9, 16, 25. These are 5 in number.

∴ Number of numbers which are not perfect squares = 30 − 5 = 25

So, the favourable number of outcomes are 25.

∴ P(drawing a card with not a perfect square number) = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{25}{30}=\frac{5}{6}$