borderline, spin again. Find the probability that the pointer will stop on an odd number or a number less than 7. 7

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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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**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!
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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