A box contains 16 cards bearing numbers 1, 2, 3, 4, …, 15, 16 respectively. A card is drawn at random from the box. What is the probability that the number on the card is:

(i) an odd number?

(ii) a prime number?

(iii) a number divisible by 3?

(iv) a number not divisible by 4?

Given,

Total number of outcomes = 16

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

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

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

∴ P(A) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{8}{16} = \dfrac{1}{2}.$

Hence, the probability of drawing an odd number is $\dfrac{1}{2}.$

(ii) Let B be the event of drawing a prime number, then

B = {2, 3, 5, 7, 11, 13}

∴ The number of favourable outcomes to the event B = 6.

∴ P(B) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{6}{16} = \dfrac{3}{8}.$

Hence, the probability of drawing a prime number is $\dfrac{3}{8}.$

(iii) Let C be the event of drawing a number divisible by 3, then

C = {3, 6, 9, 12, 15}

∴ The number of favourable outcomes to the event C = 5.

∴ P(C) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{5}{16}$

Hence, the probability of drawing a number divisible by 3 is $\dfrac{5}{16}.$

(iv) Let D be the event of drawing a number not divisible by 4, then

D = {1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15}

∴ The number of favourable outcomes to the event D = 12.

∴ P(D) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{12}{16} = \dfrac{3}{4}$

Hence, the probability of drawing a number not divisible by 4 is $\dfrac{3}{4}.$