Question

A box contains 20 cards numbered from 1 to 20. A card is drawn at random from the box.

Find the probability that the number on the drawn card is

(i) Divisible by 2 or 3

(ii) A prime number

Answer 1

Total number of cards = 20

(i) Numbers divisible by 2 or 3 are 2,3,4,6,8,9,10,12,14,15,16,18and 20.

Total favorable number of cards =13

Probability that the number on the drawn card is divisible by 2 or 3=$\left(\frac{Totalfavorablenumberofcards}{Totalnumberofcards}\right)=\frac{13}{20}$

(ii) Prime numbers are 2, 3, 5, 7, 11, 13,17and19

Total favorable number of cards = 8

Probability that the number on the drawn card is a prime number=

$\left(\frac{Totalfavorablenumberofcards}{Totalnumberofcards}\right)=\frac{8}{20}=\frac{2}{5}$