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$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)
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.
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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