$6 $ 5 For the wheel pictured on the right, assume that a person spins the pointer and is awarded the amount indicated by the pointer. Determine the person's expectation assuming the spinner has not yet been spun. $6 $5 Question content area bottom Part 1 What is the expectation? $ enter your response here (Simplify your answer. Type an integer or a decimal.)
$6 $ 5 For the wheel pictured on the right, assume that a person spins the pointer and is awarded the amount indicated by the pointer. Determine the person's expectation assuming the spinner has not yet been spun. $6 $5 Question content area bottom Part 1 What is the expectation? $ enter your response here (Simplify your answer. Type an integer or a decimal.)
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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![**Image Title: Calculating Expectation with a Spinner**
**Description:**
In the diagram, there is a wheel divided into two equal sections. The sections are labeled with monetary amounts: $6 and $5. The wheel has an arrow pointer at the center that spins to indicate a prize.
**Instructions:**
For the wheel pictured, assume that a person spins the pointer and is awarded the amount indicated by the pointer. Determine the person’s expectation assuming the spinner has not yet been spun.
**Prize Options:**
- $6
- $5
**Question:**
Part 1: What is the expected monetary value?
**Response Area:**
Enter your response here (simplify your answer by typing an integer or a decimal):
$________
**Explanation:**
To find the expectation, calculate the average value of a spin by considering each prize's probability. Each section of this spinner is equally likely to occur since they are of equal size.
1. Calculate the expected value using the formula:
\[
\text{Expected Value} = (\text{Probability of } \$6) \times \$6 + (\text{Probability of } \$5) \times \$5
\]
2. Since each outcome has an equal probability of \( \frac{1}{2} \), the calculation will be:
\[
\text{Expected Value} = \frac{1}{2} \times 6 + \frac{1}{2} \times 5
\]
3. Simplify:
\[
\text{Expected Value} = 3 + 2.5 = 5.5
\]
Therefore, write your result as $5.5.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F080f0c26-41d8-4a32-abba-3e9568242516%2Ff2d3ce34-eb65-49c1-af51-78c2c4672cb3%2F37x9wi_processed.png&w=3840&q=75)
Transcribed Image Text:**Image Title: Calculating Expectation with a Spinner**
**Description:**
In the diagram, there is a wheel divided into two equal sections. The sections are labeled with monetary amounts: $6 and $5. The wheel has an arrow pointer at the center that spins to indicate a prize.
**Instructions:**
For the wheel pictured, assume that a person spins the pointer and is awarded the amount indicated by the pointer. Determine the person’s expectation assuming the spinner has not yet been spun.
**Prize Options:**
- $6
- $5
**Question:**
Part 1: What is the expected monetary value?
**Response Area:**
Enter your response here (simplify your answer by typing an integer or a decimal):
$________
**Explanation:**
To find the expectation, calculate the average value of a spin by considering each prize's probability. Each section of this spinner is equally likely to occur since they are of equal size.
1. Calculate the expected value using the formula:
\[
\text{Expected Value} = (\text{Probability of } \$6) \times \$6 + (\text{Probability of } \$5) \times \$5
\]
2. Since each outcome has an equal probability of \( \frac{1}{2} \), the calculation will be:
\[
\text{Expected Value} = \frac{1}{2} \times 6 + \frac{1}{2} \times 5
\]
3. Simplify:
\[
\text{Expected Value} = 3 + 2.5 = 5.5
\]
Therefore, write your result as $5.5.
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