Question 1 You have a standard deck of playing cards (52 cards, 4 suits). What is the probability that you will draw a 7? Edit View Insert Format Tools Table
Question 1 You have a standard deck of playing cards (52 cards, 4 suits). What is the probability that you will draw a 7? Edit View Insert Format Tools Table
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.CR: Chapter Review
Problem 78E
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![**Question 1**
You have a standard deck of playing cards (52 cards, 4 suits). What is the probability that you will draw a 7?
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*Explanation:*
In a standard deck of 52 playing cards, there are four suits (hearts, diamonds, clubs, spades), and each suit contains one card of each value. Therefore, there are four 7s in the deck (one per suit).
**Probability Calculation:**
1. Identify the total number of favorable outcomes. In this case, it is the 4 cards that are 7s.
2. Identify the total number of possible outcomes. There are 52 cards in total.
Using the formula for probability:
\[ P(\text{drawing a 7}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{4}{52} = \frac{1}{13} \]
The probability of drawing a 7 from a standard deck of cards is \( \frac{1}{13} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faea0cfeb-d759-4aa5-b2d1-0111d15ac639%2F1affdee4-c81d-44e9-8591-ce149d49a068%2Fr2537e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 1**
You have a standard deck of playing cards (52 cards, 4 suits). What is the probability that you will draw a 7?
---
*Explanation:*
In a standard deck of 52 playing cards, there are four suits (hearts, diamonds, clubs, spades), and each suit contains one card of each value. Therefore, there are four 7s in the deck (one per suit).
**Probability Calculation:**
1. Identify the total number of favorable outcomes. In this case, it is the 4 cards that are 7s.
2. Identify the total number of possible outcomes. There are 52 cards in total.
Using the formula for probability:
\[ P(\text{drawing a 7}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{4}{52} = \frac{1}{13} \]
The probability of drawing a 7 from a standard deck of cards is \( \frac{1}{13} \).
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