Cards bearing numbers 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card which is:

(i) a prime number

(ii) a number divisible by 4

(iii) a number that is a multiple of 6

(iv) an odd number

Given,

Cards in the bag:

Sample space = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}.

Total number of outcomes = 10

(i) Let A be the event of drawing a card with prime number, then

A = {2}

∴ The number of favourable outcomes to the event A = 1

∴ P(A) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{1}{10}$

Hence, the probability of drawing a card with prime number is $\dfrac{1}{10}$.

(ii) Let B be the event of drawing a card with number divisible by 4, then

B = {4, 8, 12, 16, 20}

∴ The number of favourable outcomes to the event B = 5

∴ P(B) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{5}{10} = \dfrac{1}{2}$

Hence, the probability of drawing a card with number divisible by 4 is $\dfrac{1}{2}$.

(iii) Let C be the event of drawing a card with multiple of 6, then

C = {6, 12, 18}

∴ The number of favourable outcomes to the event C = 3

∴ P(C) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{3}{10}$

Hence, the probability of drawing a card with multiple of 6 is $\dfrac{3}{10}$.

(iv) Let D be the event of drawing a card with an odd number, then

D = ∅

∴ The number of favourable outcomes to the event D = 0

∴ P(D) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{0}{10} = 0$

Hence, the probability of drawing a card with an odd number is 0.