One card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of drawing:

(i) an ace

(ii) a 5 of a red suit

(iii) a black queen

(iv) a jack of spades

(v) a 10 of hearts

(vi) a face card

Given,

Total number of outcomes = 52

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

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

∴ P(A) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{4}{52} = \dfrac{1}{13}$

Hence, the probability of getting an ace is $\dfrac{1}{13}$.

(ii) Let B be the event of getting 5 of red suit, then

∴ The number of favourable outcomes to the event B = 2

∴ P(B) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{2}{52} = \dfrac{1}{26}$

Hence, the probability of getting 5 of red suit is $\dfrac{1}{26}$.

(iii) Let C be the event of getting a black queen, then

∴ The number of favourable outcomes to the event C = 2 (one of club and one of spade)

∴ P(C) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{2}{52} = \dfrac{1}{26}$

Hence, the probability of getting a black queen is $\dfrac{1}{26}$.

(iv) Let D be the event of getting a jack of spades, then

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

∴ P(D) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{1}{52}$

Hence, the probability of getting a jack of spades is $\dfrac{1}{52}$.

(v) Let E be the event of getting a 10 of hearts, then

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

∴ P(E) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{1}{52}$

Hence, the probability of getting a 10 of hearts is $\dfrac{1}{52}$.

(vi) Let F be the event of getting a face card, then

There are 12 face cards in a deck.

∴ The number of favourable outcomes to the event F = 12

∴ P(F) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{12}{52} = \dfrac{3}{13}$.

Hence, the probability of getting a face card is $\dfrac{3}{13}$.