probability that the arrow will land on a region lettered C and then a G?
Chapter4: Fractions
Section4.1: Visualize Fractions
Problem 75E: Give an example from your life experience (outside of school) where it was important to understand...
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Transcribed Image Text:This image features a multiple-choice question with four options, each having a fraction next to it. Here is the transcribed text for educational purposes:
---
**Question:**
Select the correct option for the given problem.
**Options:**
1. \( \frac{1}{16} \)
2. \( \frac{1}{64} \)
3. \( \frac{1}{4} \)
4. \( \frac{1}{8} \)
---
This layout represents a standard format seen in multiple-choice questions and tests. Each option is prefixed with a number followed by the corresponding fraction. This type of question is commonly used in mathematics education to assess understanding of fractions and their relative magnitudes.
Transcribed Image Text:**Educational Content on Probability and Spinners**
**Understanding the Spinner:**
In this exercise, we examine a spinner that is divided into eight equal regions. The spinner is used to understand basic probability concepts.
**Spinner Description:**
The spinner is sectioned into eight equal parts, each labeled with a different letter:
- A
- B
- C
- D
- E
- F
- G
- H
**Diagram Explanation:**
The diagram displays a circular spinner divided into 8 equal slices, each labeled from A to H in a clockwise direction. An arrow in the center points towards the edge of the circle, indicating the result of each spin.
**Probability Question:**
The question presented is: "If Rob spins the spinner twice, what is the probability that the arrow will land on a region lettered 'C' and then on a region lettered 'G'?"
**Solution:**
1. **Calculate the Probability for the First Spin (landing on 'C'):**
- Since one out of the eight regions is labeled 'C':
- Probability of landing on 'C' = 1/8
2. **Calculate the Probability for the Second Spin (landing on 'G'):**
- Since one out of the eight regions is labeled 'G':
- Probability of landing on 'G' = 1/8
3. **Determine the Combined Probability:**
- Since both events (landing on 'C' and then 'G') are independent, the combined probability can be calculated by multiplying the probabilities of each event:
- Combined Probability = Probability of first event x Probability of second event
- Combined Probability = (1/8) x (1/8)
- Combined Probability = 1/64
**Conclusion:**
The probability that Rob will spin the spinner and land on 'C' first and then on 'G' in his second spin is 1/64. This demonstrates how probabilities are multiplied in independent events.
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