.What is the probability of drawing an ace OR red king from a standard 52-card deck?
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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![### Calculating Probability in a Standard Deck of Cards
**Question:**
What is the probability of drawing an ace OR a red king from a standard 52-card deck?
**Detailed Explanation:**
To determine the probability of drawing an ace or a red king from a standard deck of 52 cards, we need to account for all possible successful outcomes and then divide by the total number of possible outcomes.
#### Step-by-Step Solution:
1. **Determine the Total Number of Cards:**
- A standard deck has 52 cards.
2. **Identify the Successful Outcomes:**
- There are 4 aces in the deck (one for each suit: hearts, diamonds, clubs, and spades).
- There are 2 red kings in the deck (one for hearts and one for diamonds).
3. **Calculate the Total Number of Successful Outcomes:**
- Total aces: 4
- Total red kings: 2
- Since aces and red kings are distinct cards, there is no overlap to worry about.
- Therefore, the total number of successful outcomes = 4 (aces) + 2 (red kings) = 6
4. **Calculate the Probability:**
\[
\text{Probability} = \frac{\text{Number of Successful Outcomes}}{\text{Total Number of Outcomes}} = \frac{6}{52} = \frac{3}{26}
\]
Thus, the probability of drawing an ace OR a red king from a standard deck of 52 cards is \(\frac{3}{26}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e662ae8-5544-47c6-b13f-443ca92f6b6f%2F0c8a4155-4090-4b97-a0a4-5ded88bb2cd0%2F3rnr92c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculating Probability in a Standard Deck of Cards
**Question:**
What is the probability of drawing an ace OR a red king from a standard 52-card deck?
**Detailed Explanation:**
To determine the probability of drawing an ace or a red king from a standard deck of 52 cards, we need to account for all possible successful outcomes and then divide by the total number of possible outcomes.
#### Step-by-Step Solution:
1. **Determine the Total Number of Cards:**
- A standard deck has 52 cards.
2. **Identify the Successful Outcomes:**
- There are 4 aces in the deck (one for each suit: hearts, diamonds, clubs, and spades).
- There are 2 red kings in the deck (one for hearts and one for diamonds).
3. **Calculate the Total Number of Successful Outcomes:**
- Total aces: 4
- Total red kings: 2
- Since aces and red kings are distinct cards, there is no overlap to worry about.
- Therefore, the total number of successful outcomes = 4 (aces) + 2 (red kings) = 6
4. **Calculate the Probability:**
\[
\text{Probability} = \frac{\text{Number of Successful Outcomes}}{\text{Total Number of Outcomes}} = \frac{6}{52} = \frac{3}{26}
\]
Thus, the probability of drawing an ace OR a red king from a standard deck of 52 cards is \(\frac{3}{26}\).
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