A box contains 20 balls bearing numbers 1, 2, 3, 4, ……, 20. A ball is drawn at random from the box. What is the probability that the number on the ball is

(i) an odd number

(ii) divisible by 2 or 3

(iii) prime number

(iv) not divisible by 10?

A ball is drawn at random from the box it means that all outcomes are equally likely.

Sample space = {1, 2, 3, ……, 20}, which has 20 equally likely outcomes.

(i) Let A be the event 'the number on the ball is odd', then

A = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}.

∴ The number of favourable outcomes to the event A = 10.

∴ P(odd number) = $\dfrac{10}{20} = \dfrac{1}{2}.$

Hence, the probability that the ball drawn has an odd number is $\dfrac{1}{2}.$

(ii) Let B be the event 'the number on the ball is divisible by 2 or 3', then

B = {2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20}.

∴ The number of favourable outcomes to the event B = 13.

∴ P(number is divisible by 2 or 3) = $\dfrac{13}{20}.$

Hence, the probability that the ball drawn has a number that is divisible by 2 or 3 is $\dfrac{13}{20}.$

(iii) Let C be the event 'the number on the ball is prime', then

C = {2, 3, 5, 7, 11, 13, 17, 19}.

∴ The number of favourable outcomes to the event C = 8.

∴ P(prime number) = $\dfrac{8}{20} = \dfrac{2}{5}.$

Hence, the probability that the ball drawn has a prime number is $\dfrac{2}{5}.$

(iv) Let D be the event 'the number on the ball is not divisible by 10', then

D = {1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19}.

∴ The number of favourable outcomes to the event D = 18.

∴ P(number is not divisible by 10) = $\dfrac{18}{20} = \dfrac{9}{10}.$

Hence, the probability that the ball drawn has a number that is not divisible by 10 is $\dfrac{9}{10}.$