Question

 What is the probability of drawing a king or a heart from a deck of cards ?

• A. \(\frac{1}{13}\)
• B. \(\frac{4}{13}\)
• C. \(\frac{15}{17}\)
• D. \(\frac{1}{52}\)

Answer 1

The Correct Option is B

To find the probability of drawing a king or a heart from a standard deck of cards, we can use the principle of probability and the concept of mutually exclusive events. Here's how we solve this step-by-step:

1. A standard deck of cards has 52 cards, comprising four suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards.
2. We need to find the probability of drawing a king or a heart. These are two separate events, but there is an overlap because the king of hearts belongs to both events.
3. Calculate the probability of drawing a king:
   • There are 4 kings in total (one from each suit).
   • Probability of drawing a king: \(\frac{4}{52}\).
4. Calculate the probability of drawing a heart:
   • There are 13 hearts in total.
   • Probability of drawing a heart: \(\frac{13}{52}\).
5. Calculate the probability of drawing the king of hearts, as it's counted in both previous probabilities:
   • Probability of drawing the king of hearts: \(\frac{1}{52}\).
6. Apply the formula for the probability of either event A or B happening: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
   • Here, \(A\) is drawing a king and \(B\) is drawing a heart.
   • So, \[ P(\text{King or Heart}) = \frac{4}{52} + \frac{13}{52} - \frac{1}{52} \]
   • By simplifying: \[ P(\text{King or Heart}) = \frac{16}{52} = \frac{4}{13} \]

Therefore, the probability of drawing a king or a heart from a deck of cards is \(\frac{4}{13}\), which matches the correct answer given in the options.