You randomly select one card from a 52-card deck. Find the probability of selecting a red five or a red six.
You randomly select one card from a 52-card deck. Find the probability of selecting a red five or a red six.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![**Card Probability Problem**
You randomly select one card from a 52-card deck. Find the probability of selecting a red five or a red six.
**The probability is** [ ] (Type an integer or a fraction. Simplify your answer.)
---
**Explanation:**
In a standard 52-card deck, there are two red suits: hearts and diamonds. Each suit has one five and one six, giving us the red cards:
- Red five: hearts and diamonds
- Red six: hearts and diamonds
Total favorable outcomes for red five or red six = 2 (five) + 2 (six) = 4 cards.
To calculate probability:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{4}{52} = \frac{1}{13} \]
Therefore, the simplified probability of selecting a red five or a red six is \(\frac{1}{13}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8470e22-cdb6-4814-babe-099f6875e962%2Fe8fa8d7d-f962-40c6-93a9-8bcc4bcc9af7%2Fdkf8nk8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Card Probability Problem**
You randomly select one card from a 52-card deck. Find the probability of selecting a red five or a red six.
**The probability is** [ ] (Type an integer or a fraction. Simplify your answer.)
---
**Explanation:**
In a standard 52-card deck, there are two red suits: hearts and diamonds. Each suit has one five and one six, giving us the red cards:
- Red five: hearts and diamonds
- Red six: hearts and diamonds
Total favorable outcomes for red five or red six = 2 (five) + 2 (six) = 4 cards.
To calculate probability:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{4}{52} = \frac{1}{13} \]
Therefore, the simplified probability of selecting a red five or a red six is \(\frac{1}{13}\).
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