The odds of an event occurring are 3:5. Find (a) the probability that the event will occur and (b) the probability that the event will not occur. (a) The probability that the event will occur is 0.375 (Type an integer or decimal rounded to the nearest thousandth as needed.) (b) The probability that the event will not occur is 0.625. (Type an integer or decimal rounded to the nearest thousandth as needed.)
The odds of an event occurring are 3:5. Find (a) the probability that the event will occur and (b) the probability that the event will not occur. (a) The probability that the event will occur is 0.375 (Type an integer or decimal rounded to the nearest thousandth as needed.) (b) The probability that the event will not occur is 0.625. (Type an integer or decimal rounded to the nearest thousandth as needed.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Understanding Odds and Probabilities in Gambling
In gambling, the chances of winning are often expressed in terms of odds rather than probabilities. It is crucial to differentiate between these two concepts to comprehend the likelihood of outcomes accurately.
#### Definition of Odds:
- **Odds of Winning**: The ratio of the number of successful outcomes to the number of unsuccessful outcomes.
- **Odds of Losing**: The ratio of the number of unsuccessful outcomes to the number of successful outcomes.
#### Example:
If the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, then:
- The odds of winning are 2:3 (read as "2 to 3") or \(\frac{2}{3}\).
- The odds of losing are 3:2 (read as "3 to 2") or \(\frac{3}{2}\).
**Note:** If the odds of winning are \(\frac{2}{3}\), the probability of success can be calculated using the formula:
\[ \text{Probability of Success} = \frac{\text{number of successful outcomes}}{\text{number of successful outcomes} + \text{number of unsuccessful outcomes}} = \frac{2}{5} \]
### Calculating Probabilities from Given Odds:
#### Problem Statement:
Given the odds of an event occurring are 3:5. Find:
a) The probability that the event will occur.
b) The probability that the event will not occur.
#### Solution:
1. **Calculate the Probability that the Event Will Occur:**
\[
\text{Probability} = \frac{\text{successful outcomes}}{\text{successful outcomes + unsuccessful outcomes}} = \frac{3}{3+5} = \frac{3}{8} = 0.375
\]
The probability that the event will occur is **0.375**.
*(Type an integer or decimal rounded to the nearest thousandth as needed.)*
2. **Calculate the Probability that the Event Will Not Occur:**
\[
\text{Probability} = \frac{\text{unsuccessful outcomes}}{\text{successful outcomes + unsuccessful outcomes}} = \frac{5}{3+5} = \frac{5}{8} = 0.625
\]
The probability that the event will not occur is **0.625**.
*(Type an integer or decimal rounded](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09dd8e29-942c-4a28-8d6e-4fa3e84656fc%2F8ab6bb11-9449-4065-ac18-a3a71650a54d%2Fana54q_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Odds and Probabilities in Gambling
In gambling, the chances of winning are often expressed in terms of odds rather than probabilities. It is crucial to differentiate between these two concepts to comprehend the likelihood of outcomes accurately.
#### Definition of Odds:
- **Odds of Winning**: The ratio of the number of successful outcomes to the number of unsuccessful outcomes.
- **Odds of Losing**: The ratio of the number of unsuccessful outcomes to the number of successful outcomes.
#### Example:
If the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, then:
- The odds of winning are 2:3 (read as "2 to 3") or \(\frac{2}{3}\).
- The odds of losing are 3:2 (read as "3 to 2") or \(\frac{3}{2}\).
**Note:** If the odds of winning are \(\frac{2}{3}\), the probability of success can be calculated using the formula:
\[ \text{Probability of Success} = \frac{\text{number of successful outcomes}}{\text{number of successful outcomes} + \text{number of unsuccessful outcomes}} = \frac{2}{5} \]
### Calculating Probabilities from Given Odds:
#### Problem Statement:
Given the odds of an event occurring are 3:5. Find:
a) The probability that the event will occur.
b) The probability that the event will not occur.
#### Solution:
1. **Calculate the Probability that the Event Will Occur:**
\[
\text{Probability} = \frac{\text{successful outcomes}}{\text{successful outcomes + unsuccessful outcomes}} = \frac{3}{3+5} = \frac{3}{8} = 0.375
\]
The probability that the event will occur is **0.375**.
*(Type an integer or decimal rounded to the nearest thousandth as needed.)*
2. **Calculate the Probability that the Event Will Not Occur:**
\[
\text{Probability} = \frac{\text{unsuccessful outcomes}}{\text{successful outcomes + unsuccessful outcomes}} = \frac{5}{3+5} = \frac{5}{8} = 0.625
\]
The probability that the event will not occur is **0.625**.
*(Type an integer or decimal rounded
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