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8. Suppose you draw one card from a deck of 52 cards. What is the probability of drawing a club or a face card?

Ask by Elliott Stuart. in the United States
Feb 26,2025

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Answer

The probability of drawing a club or a face card is 11/26.

Solution

To determine the probability of drawing a club or a face card from a standard deck of 52 cards, we can use the principle of inclusion and exclusion. Step 1: Count the number of clubs. • There are 13 clubs in the deck. Step 2: Count the number of face cards. • There are 12 face cards in the deck (jack, queen, and king in each of the 4 suits). Step 3: Count the number of cards that are both clubs and face cards. • In the clubs, there are 3 face cards (jack, queen, and king of clubs). Step 4: Use the formula for the union of two events:   Number of favorable outcomes = (Number of clubs) + (Number of face cards) – (Number of club face cards)   = 13 + 12 – 3   = 22 Step 5: Calculate the probability:   Probability = 22/52   Simplify by dividing numerator and denominator by 2:   = 11/26 Thus, the probability of drawing a club or a face card is 11/26.

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Mind Expander

To determine the probability of drawing a club or a face card, you need to consider both categories: there are 13 clubs in a deck and 12 face cards (3 for each of the 4 suits: King, Queen, Jack). However, one of the face cards (the King of clubs) is counted in both categories, so you have 13 + 12 - 1 = 24 favorable outcomes. The probability is therefore 24/52, which simplifies to 6/13! When you think about probabilities, consider playing card games! Understanding the odds can give you a competitive edge. For example, if you're playing poker, knowing the probability of drawing certain hands can help you decide whether to bet, call, or fold—turning the likelihood of drawing those hands into strategic decisions at the table!

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