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9. Find the probability of choosing a heart or and ace card when a card is drawn at random from a deck of 52 cards.

9. Find the probability of choosing a heart or and ace card when a card is drawn at random from a deck of 52 cards.

Algebra and Trigonometry (6th Edition)
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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**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 \( \frac{4}{13} \).
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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