There are 25 discs numbered 1 to 25. They are put in a closed box and shaken thoroughly. A disc is drawn at random from the box. Find the probability that the number on the disc is:

(i) an odd number

(ii) divisible by 2 and 3 both

(iii) a number less than 16

Given,

There are 25 discs numbered from 1 to 25.

Sample space:S={1, 2, 3, …, 25}

Total number of outcomes = 25

(i) Let A be the event of getting an odd number, then

A = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25}

∴ The number of favourable outcomes to the event A = 13

∴ P(A) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{13}{25}$

Hence, the probability of getting an odd number is $\dfrac{13}{25}$.

(ii) Let B be the event of getting a number divisible by both 2 and 3, then

B = {6, 12, 18, 24}

∴ The number of favourable outcomes to the event B = 4

∴ P(B) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{4}{25}$

Hence, the probability of getting a number divisible by both 2 and 3 is $\dfrac{4}{25}$.

(iii) Let C be the event of getting a number less than 16, then

C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}

∴ The number of favourable outcomes to the event C = 15

∴ P(C) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{15}{25} = \dfrac{3}{5}$

Hence, the probability of getting a number less than 16 is $\dfrac{3}{5}$.