A card is drawn from a standard deck of 52 cards. What is the probability that the card is a diamond or a king?

• A. $0.33$
• B. $0.31$
• C. $0.15$
• D. $0.85$

Answer: (B)

Verified step by step guidance

1. Identify the total number of possible outcomes. A standard deck has 52 cards, so there are 52 possible outcomes when drawing a card.
2. Determine the number of favorable outcomes for drawing a diamond. There are 13 diamonds in a deck.
3. Determine the number of favorable outcomes for drawing a king. There are 4 kings in a deck.
4. Since the king of diamonds is counted in both the diamonds and kings, use the principle of inclusion-exclusion to avoid double-counting. Calculate the probability of drawing a diamond or a king using the formula: P(Diamond or King) = P(Diamond) + P(King) - P(Diamond and King).
5. Express the probabilities as fractions: P(Diamond) = 13/52, P(King) = 4/52, and P(Diamond and King) = 1/52. Substitute these values into the formula to find the probability of drawing a diamond or a king.