One card is drawn from a wall shuffled deck of 52 cards. Find the probability of getting a king of red colour

Question

Accepted Answer

To determine the probability of drawing a king of red color from a well-shuffled deck of 52 cards, we need to consider the composition of the deck and the specific criteria for the card we are interested in.

1. **Composition of the Deck:**
   - A standard deck of 52 cards consists of 4 suits: hearts, diamonds, clubs, and spades.
   - Each suit contains 13 cards, including one king.
   - The red suits are hearts and diamonds.

2. **Number of Red Kings:**
   - There are 2 red suits (hearts and diamonds), and each suit has one king.
   - Therefore, there are 2 red kings in the deck.

3. **Probability Calculation:**
   - The probability of drawing a specific card from the deck is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
   - The number of favorable outcomes (drawing a red king) is 2.
   - The total number of possible outcomes (drawing any card) is 52.

$$
   \text{Probability of drawing a red king} = \frac{\text{Number of red kings}}{\text{Total number of cards}} = \frac{2}{52} = \frac{1}{26}
   $$

Therefore, the probability of drawing a king of red color is $\frac{1}{26}$, which corresponds to Option 2.

**Explanation of Incorrect Options:**

- **Option 1: $\frac{3}{13}$**
  - This option suggests a higher probability than is possible for drawing a specific card type from a deck. It does not accurately reflect the number of red kings relative to the total number of cards.

- **Option 3: $\frac{3}{26}$**
  - This option implies there are more favorable outcomes than actually exist. There are only 2 red kings, not 3, so this probability is incorrect.

- **Option 4: $\frac{2}{13}$**
  - This option suggests a probability that is too high. It would be correct if there were 4 red kings in the deck, but since there are only 2, this option is incorrect.

In conclusion, Option 2 ($\frac{1}{26}$) is the correct answer, as it accurately represents the probability of drawing a king of red color from a standard deck of 52 cards.