Question

4. Suppose you draw one card from a deck of 52 cards. What is the probability of drawing a face card or a 5?

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

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Tutor-Verified Answer

Answer

The probability of drawing a face card or a 5 is 4/13.

Solution

There are 12 face cards in a standard deck (Jack, Queen, King for each of the 4 suits) and 4 cards that are 5's (one for each suit). Since a 5 is not a face card, these outcomes are mutually exclusive. Therefore, the total number of favorable outcomes is 12 + 4 = 16. The probability is calculated as follows:  Probability = (Number of favorable outcomes) / (Total number of cards)  Probability = 16/52 Simplify by dividing both numerator and denominator by 4:  16/52 = 4/13 Thus, the probability of drawing a face card or a 5 is 4/13.

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Bonus Knowledge

In a standard deck of 52 playing cards, there are 3 face cards in each of the 4 suits: King, Queen, and Jack, totaling 12 face cards. Additionally, there are 4 cards with the value of 5 (one from each suit). Therefore, there are 12 face cards plus 4 fives, which totals 16. However, since there are no overlapping cards between face cards and fives, the probability of drawing either a face card or a 5 is calculated as the number of favorable outcomes divided by the total outcomes: \( \frac{16}{52} \) which simplifies to \( \frac{4}{13} \). Now, let’s think practically about card games! Knowing the probability of drawing specific cards can give you an edge when playing games like Poker or Blackjack. Understanding these probabilities helps you make better decisions such as whether to bet, fold, or hit, making the game not only strategic but also so much more exciting! Additionally, if you're a fan of games, consider dabbling in some fun card games such as Rummy or Cribbage, where knowing the probability of drawing certain cards can not only enhance your game but also impress your friends! Each game has its unique twists and strategies that keep things interesting and engaging.

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