One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting
(i) a king of red colour
(ii) a face card
(iii) a red face card
(iv)the jack of hearts
(v) a spade
(vi) the queen of diamonds
Answer:
(i) Probability of getting a king of red colour:
There are 2 red kings in the deck: the King of Hearts and the King of Diamonds.
- Favorable outcomes = 2 (King of Hearts, King of Diamonds)
- Total outcomes = 52
P(king of red colour) = 2/52 = 1/26
(ii) Probability of getting a face card:
Face cards include the Jack, Queen, and King in each suit. There are 3 face cards per suit, and 4 suits in total.
- Favorable outcomes = 3 face cards × 4 suits = 12
- Total outcomes = 52
P(face card)=12/52 = 3/13
(iii) Probability of getting a red face card:
Red suits are Hearts and Diamonds, and each has 3 face cards (Jack, Queen, King).
- Favorable outcomes = 3 face cards × 2 red suits = 6
- Total outcomes = 52
P(red face card) = 6/52 = 3/26
(iv) Probability of getting the jack of hearts:
There is only one Jack of Hearts in the deck.
- Favorable outcomes = 1 (Jack of Hearts)
- Total outcomes = 52
P(jack of hearts) = 1/52
(v) Probability of getting a spade:
There are 13 spades in the deck (one for each rank: Ace to King).
- Favorable outcomes = 13 (spades)
- Total outcomes = 52
P(spade)=13/52 = 1/4
(vi) Probability of getting the queen of diamonds:
There is only one Queen of Diamonds in the deck.
- Favorable outcomes = 1 (Queen of Diamonds)
- Total outcomes = 52
P(queen of diamonds) = 1/52