Question

One card is selected at random from a well-shuffled deck of 52 cards. What is the probability of getting a red coloured king?

• A. \( \frac{1}{13} \)
• B. \( \frac{2}{13} \)
• C. \( \frac{1}{26} \)
• D. \( \frac{1}{52} \)

Hint:

Always remember:
• Total cards = 52
• Red cards = 26
• Kings = 4
• Red Kings = 2 These standard card facts appear very frequently in probability questions.

Answer 1

The Correct Option is C

Concept: A standard deck of playing cards contains: \[ 52 \text{ cards} \] These cards are divided into 4 suits: \[ \text{Hearts},\ \text{Diamonds},\ \text{Spades},\ \text{Clubs} \] Each suit contains: \[ 13 \text{ cards} \] Important facts:
• Hearts and Diamonds are red suits.
• Spades and Clubs are black suits.
• Each suit contains exactly one King.

Step 1: Determine total possible outcomes. One card is selected from 52 cards. Therefore: \[ n(S) = 52 \]

Step 2: Identify favorable outcomes. We need a red coloured king. Red suits are: \[ \text{Hearts and Diamonds} \] So favorable cards are:
• King of Hearts
• King of Diamonds Hence: \[ n(E) = 2 \]

Step 3: Apply probability formula. \[ P(E) = \frac{n(E)}{n(S)} \] Substitute values: \[ P(E) = \frac{2}{52} \]

Step 4: Simplify the fraction. Divide numerator and denominator by 2: \[ P(E) = \frac{1}{26} \]

Step 5: Verification and understanding. There are: \[ 4 \text{ kings total} \] Among them: \[ 2 \text{ are red}, \quad 2 \text{ are black} \] Thus probability of selecting a red king from the full deck is: \[ \frac{2}{52} = \frac{1}{26} \] Final Answer: \[ \boxed{\frac{1}{26}} \]