Math Problem Statement
If one card is randomly selected from a well-shuffled standard deck of 52 cards, what is the probability that the card selected is a heart? Leave your answer as a reduced fraction.
Solution
A standard deck of 52 cards contains 4 suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards.
To find the probability of selecting a heart, we use the formula for probability:
- Number of favorable outcomes (hearts) = 13
- Total number of outcomes (cards in the deck) = 52
Thus, the probability is:
Now, we reduce the fraction by dividing both the numerator and denominator by 13:
Therefore, the probability of selecting a heart is .
Would you like further details or have any questions?
Here are 5 related questions:
- What is the probability of selecting a club from the deck?
- What is the probability of drawing an Ace from the deck?
- If two cards are drawn, what is the probability that both are hearts?
- What is the probability of drawing a red card (hearts or diamonds)?
- What is the probability of drawing a face card (Jack, Queen, King)?
Tip: Always check if you can simplify a fraction by finding the greatest common divisor (GCD).
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Math Problem Analysis
Mathematical Concepts
Probability
Fractions
Reduction of Fractions
Formulas
Probability = Number of favorable outcomes / Total number of outcomes
Theorems
Basic Probability Theory
Suitable Grade Level
Grades 6-8
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