Question

A card is drawn from a deck. Probability of getting king is ____.

• A. 1/52
• B. 1/13
• C. 4/13
• D. 1/4

Hint:

In a deck of 52 cards, there are 13 different ranks (Ace through King). Since each rank appears 4 times, the probability of picking any specific rank (like a King, an 8, or an Ace) is always \( 4/52 \), which simplifies to \( 1/13 \).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Probability is the measure of the likelihood that an event will occur, calculated as the ratio of favorable outcomes to the total number of possible outcomes.

Step 2: Key Formula or Approach:
\[ P(E) = \frac{n(E)}{n(S)} \] Where \( n(E) \) is the number of kings and \( n(S) \) is the total number of cards in a standard deck.

Step 3: Detailed Explanation:
1. A standard deck of cards contains a total of 52 cards. So, \( n(S) = 52 \). 2. There are 4 suits (Hearts, Diamonds, Clubs, Spades), and each suit has exactly one King. Therefore, there are 4 Kings in total. So, \( n(E) = 4 \). 3. The probability of drawing a King is: \[ P(\text{King}) = \frac{4}{52} \] Dividing both numerator and denominator by 4: \[ P(\text{King}) = \frac{1}{13} \]

Step 4: Final Answer:
The probability of getting a King is 1/13.

Answer 2

Instead of directly computing \( \frac{4}{52} \), we can think of the deck as split into 13 equally-sized rank groups, Aces, 2s, 3s, and so on up to Kings, each containing exactly 4 cards, one per suit. Drawing a random card is then equivalent to randomly picking one of these 13 groups.

1. 1/52: This would be the probability of drawing one specific card, for example the King of Hearts alone. Since the question asks for any King, not one particular card, this understates the true probability.
2. 1/13: There are exactly 13 rank groups in the deck, and each group is the same size, 4 cards, so each group is equally likely to be the one a random card belongs to. The King group is exactly one of these 13 equally likely groups, so the probability of drawing a card from it is \( \frac{1}{13} \).
3. 4/13: This value does not correspond to any natural count in a standard deck; it would arise from confusing the number of suits, 4, with something being divided across only 13 units in an inconsistent way, rather than correctly reflecting one group out of thirteen equally sized groups.
4. 1/4: This is the probability of drawing a card of a specific suit, for example any Spade, since each suit has 13 of the 52 cards. It is unrelated to the chance of drawing a specific rank like King.

Since the deck splits perfectly into 13 equally likely rank groups and Kings form exactly one such group, the probability works out to one in thirteen.

Therefore, the correct answer is 1/13.