4. Probability
Addition Rule
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A card is drawn from a standard deck of 52 cards. What is the probability that the card is a diamond or a king?
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Verified step by step guidance1
Identify the total number of possible outcomes. A standard deck has 52 cards, so there are 52 possible outcomes when drawing a card.
Determine the number of favorable outcomes for drawing a diamond. There are 13 diamonds in a deck.
Determine the number of favorable outcomes for drawing a king. There are 4 kings in a deck.
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).
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.
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