Question

Cards marked with numbers 1,2,3,4,.....20 are well shuffled and a card is drawn at random. What is the probability that the number on the card is :

(i) a prime number ? (ii) divisible by 3 ? (iii) a perfect square ?

• A. (i) $\frac{2}{5}$ (ii) $\frac{3}{5}$ (iii) $\frac{3}{20}$
• B. (i) $\frac{2}{5}$ (ii) $\frac{3}{10}$ (iii) $\frac{1}{5}$
• C. (i) $\frac{1}{5}$ (ii) $\frac{1}{3}$ (iii) $\frac{3}{20}$
• D. None of the above

Answer 1

Answer: (B), (C)

The correct options are
B

(i) $\frac{2}{5}$ (ii) $\frac{3}{10}$ (iii) $\frac{1}{5}$

C

(i) $\frac{1}{5}$ (ii) $\frac{1}{3}$ (iii) $\frac{3}{20}$

Cards are marked from 1 to 20

The total number of outcomes = 20

(i) a prime number

The prime numbers between 1 and 20 are {2,3,5,7,11,13,17,19}

Hence the number favourable outcomes = 8

P(getting a prime number) = $\frac{numberoffavourableoutcomes}{totalnumberofoutcomes}$ = $\frac{8}{20}$ = $\frac{2}{5}$

(ii) Divisible by 3

The numbers divisible by 3 between 1 and 20 are {3,6,9,12,15,18}

Hence the number of numbers divisible by 3 between 1 and 20 (i.e. the number of favourable outcomes) = 6

P(getting a number divisible by 3) = $\frac{numberoffavourableoutcomes}{totalnumberofoutcomes}$ = $\frac{6}{20}$ = $\frac{3}{10}$

(iii) a perfect square

The numbers between 1 and 20 which are perfect squares are {1,4,9,16}

Hence the number of perfect squares between 1 and 20 (i.e. the number of favourable outcomes) = 4

P(getting a perfect squares) = $\frac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$ = $\frac{4}{20}$ = $\frac{1}{5}$