A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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![**Educational Website Content: Probability with Spinners**
---
**Problem Description:**
It is equally probable that the pointer on the spinner shown will land on any one of the eight regions, numbered 1 through 8. If the pointer lands on a borderline, spin again. Find the probability that the pointer will stop on an odd number or a number less than 7.
**Spinner Description:**
The spinner is divided into eight equal sections, each labeled with a number from 1 to 8. The numbers are arranged clockwise as follows:
- 1 (yellow)
- 2 (pink)
- 3 (blue)
- 4 (dark blue)
- 5 (green)
- 6 (light green)
- 7 (orange)
- 8 (light yellow)
The spinner includes a pointer at its center, which can land on any of these numbered sections.
**Solution:**
To determine the probability, we need to identify the favorable outcomes:
- Odd numbers: 1, 3, 5, 7
- Numbers less than 7: 1, 2, 3, 4, 5, 6
Combine these criteria to list unique favorable numbers: 1, 2, 3, 4, 5, 6, 7
Count the favorable numbers: 7
There are 8 possible outcomes altogether (numbers 1 through 8).
Thus, the probability that the pointer will stop on an odd number or a number less than 7 is given by the ratio of favorable outcomes to the total number of outcomes:
\[
\text{Probability} = \frac{7}{8}
\]
However, this example mistakenly shows the probability as \(\frac{3}{4}\), which might have been simplified incorrectly in a different context.
*Note: Always cross-check to ensure correct interpretation when given probabilities.*
---
For more detailed explanations on probabilistic concepts, continue exploring our educational resources on probability theory and statistics!](https://content.bartleby.com/qna-images/question/1a4d4bf4-ffa5-40bf-a4b6-a19d4afcfff5/9d5aedff-1f8e-45a1-8a3b-f149803070d7/m0bry9l_processed.png)
Transcribed Image Text:**Educational Website Content: Probability with Spinners**
---
**Problem Description:**
It is equally probable that the pointer on the spinner shown will land on any one of the eight regions, numbered 1 through 8. If the pointer lands on a borderline, spin again. Find the probability that the pointer will stop on an odd number or a number less than 7.
**Spinner Description:**
The spinner is divided into eight equal sections, each labeled with a number from 1 to 8. The numbers are arranged clockwise as follows:
- 1 (yellow)
- 2 (pink)
- 3 (blue)
- 4 (dark blue)
- 5 (green)
- 6 (light green)
- 7 (orange)
- 8 (light yellow)
The spinner includes a pointer at its center, which can land on any of these numbered sections.
**Solution:**
To determine the probability, we need to identify the favorable outcomes:
- Odd numbers: 1, 3, 5, 7
- Numbers less than 7: 1, 2, 3, 4, 5, 6
Combine these criteria to list unique favorable numbers: 1, 2, 3, 4, 5, 6, 7
Count the favorable numbers: 7
There are 8 possible outcomes altogether (numbers 1 through 8).
Thus, the probability that the pointer will stop on an odd number or a number less than 7 is given by the ratio of favorable outcomes to the total number of outcomes:
\[
\text{Probability} = \frac{7}{8}
\]
However, this example mistakenly shows the probability as \(\frac{3}{4}\), which might have been simplified incorrectly in a different context.
*Note: Always cross-check to ensure correct interpretation when given probabilities.*
---
For more detailed explanations on probabilistic concepts, continue exploring our educational resources on probability theory and statistics!
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