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
Step-by-Step Solution
Key Concept: For an experiment with equally likely outcomes, the probability of an event = (Number of favourable outcomes) ÷ (Total number of outcomes). In a standard deck there are 52 cards, 13 cards in each of the four suits (hearts, diamonds, clubs, spades). Face cards are Jacks, Queens and Kings.
1. Total number of equally likely outcomes = 52 (the whole deck).
2. (i) King of red colour
- Red suits = hearts and diamonds. Each red suit contains exactly one king.
- Favourable cards = 2 (King of hearts, King of diamonds).
- Probability $P = \dfrac{2}{52}=\dfrac{1}{26}$.
3. (ii) A face card
- Face cards = Jack, Queen, King. 3 per suit × 4 suits = 12 cards.
- $P = \dfrac{12}{52}=\dfrac{3}{13}$.
4. (iii) A red face card
- Red suits = hearts and diamonds. Each red suit has 3 face cards, so $2\times3 = 6$ cards.
- $P = \dfrac{6}{52}=\dfrac{3}{26}$.
5. (iv) The jack of hearts
- Only one specific card satisfies the condition.
- $P = \dfrac{1}{52}$.
6. (v) A spade
- Each suit has 13 cards. Hence spades = 13 cards.
- $P = \dfrac{13}{52}=\dfrac{1}{4}$.
7. (vi) The queen of diamonds
- Again a single specific card.
- $P = \dfrac{1}{52}$.
All fractions are reduced to their simplest form to obtain full marks.
Correct Answer: (i) $\dfrac{1}{26}$, (ii) $\dfrac{3}{13}$, (iii) $\dfrac{3}{26}$, (iv) $\dfrac{1}{52}$, (v) $\dfrac{1}{4}$, (vi) $\dfrac{1}{52}$