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?
[3 MARKS]

Answer 1

Each subpart: 1 Mark each

(i) Prime numbers from 1 to 20 are 2, 3, 5, 7, 11, 13, 17 and 19.
i.e., favourable outcomes = 8
$\therefore$ P(getting a prime number) $=\frac{8}{20}=\frac{2}{5}$

ii) Numbers divisible by 3 are 3, 6, 9, 12, 15 and 18
$\therefore$ P(getting a number divisible by 3)
$=\frac{6}{20}=\frac{3}{10}$

iii) Perfect squares are 1, 4, 9 and 16
$\therefore$ P(getting a perfect square)
$=\frac{4}{20}=\frac{1}{5}$