Math Problem Statement
What is the probability of drawing each of the following cards from a standard playing deck? See the entry “playing cards” in the glossary to learn what playing cards are included in a deck.
Solution
A standard deck of playing cards contains 52 cards, which are divided into four suits: Hearts, Diamonds, Clubs, and Spades. Each suit has 13 cards: Ace, 2 through 10, Jack, Queen, and King. Hearts and Diamonds are red suits, while Clubs and Spades are black suits.
Let’s go through the probability of drawing specific types of cards:
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Probability of drawing a red card:
- There are 26 red cards in total (13 Hearts + 13 Diamonds).
- The probability is:
-
Probability of drawing a face card (Jack, Queen, King):
- There are 12 face cards in total (3 face cards per suit × 4 suits).
- The probability is:
-
Probability of drawing an Ace:
- There are 4 Aces in total (one in each suit).
- The probability is:
-
Probability of drawing a specific card (e.g., the Queen of Hearts):
- There is only one Queen of Hearts in the deck.
- The probability is:
-
Probability of drawing a Spade:
- There are 13 Spades in the deck.
- The probability is:
Would you like further details or have any questions?
Additional questions:
- What is the probability of drawing two red cards consecutively without replacement?
- What is the probability of drawing a face card or a red card?
- How do probabilities change if cards are drawn with replacement?
- What is the probability of drawing a number card (2 through 10) from the deck?
- How does the probability of drawing a King compare to that of drawing a face card?
Tip: When calculating probabilities, always ensure you know whether the events are independent or dependent (with or without replacement).
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Math Problem Analysis
Mathematical Concepts
Probability
Combinatorics
Formulas
P(Event) = (Number of favorable outcomes) / (Total possible outcomes)
Theorems
Basic Probability Theorem
Suitable Grade Level
Grades 6-8
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