Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Transcribed Image Text:**Problem 9: Probability in a Standard Deck of Cards**
Find the probability of choosing a heart or an ace when a card is drawn at random from a deck of 52 cards.
**Solution Approach:**
1. **Identify the Total Number of Outcomes:**
- There are 52 cards in a standard deck.
2. **Identify the Desired Outcomes:**
- There are 13 hearts (one for each rank).
- There are 4 aces (one for each suit, including the ace of hearts).
3. **Use the Addition Rule for Probability:**
- Total the number of heart cards and ace cards; however, remember to subtract the overlap (ace of hearts) that was counted twice.
- Probability = (Number of Hearts + Number of Aces - Overlap) / Total Number of Cards
- Probability = (13 + 4 - 1) / 52
- Probability = 16 / 52
- Simplified Probability = 4 / 13
**Conclusion:**
Therefore, the probability of drawing a heart or an ace from a standard deck of 52 cards is \( \frac{4}{13} \).
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