Find the expected value (or expectation) of the games described.? Carol wins 3 if a die r

Name: Problem 5, Chapter 13: Algebra and Trigonometry
Uploaded: 2020-09-12T09:45:03-08:00
Duration: 3 min 26 s
Channel: Puneet Prajapati
Description: Find the expected value (or expectation) of the games described.? Carol wins 3 if a die roll shows a six, and she wins 0.50 otherwise.

step 1 Okay, so we will understand the concept of expected value. Now we will understand it through an

Question

Find the expected value (or expectation) of the games described.? $$ \begin{array}{l}{\text { Carol wins } \$ 3 \text { if a die roll shows a six, and she wins } \$ 0.50} \\ {\text { otherwise. }}\end{array} $$

   Find the expected value (or expectation) of the games described.?
$$
\begin{array}{l}{\text { Carol wins } \$ 3 \text { if a die roll shows a six, and she wins } \$ 0.50} \\ {\text { otherwise. }}\end{array}
$$

Algebra and Trigonometry

James Stewart,… 2nd Edition

Chapter 13, Problem 5

Instant Answer

Solved by Expert Puneet Prajapati

09/12/2020

Step 1

When Carol rolls a die, she can get any number from 1 to 6. If she rolls a 6, she wins $3. If she rolls any other number (1, 2, 3, 4, or 5), she wins $0.50. Show more…

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Find the expected value (or expectation) of the games described.? $$ \begin{array}{l}{\text { Carol wins } \$ 3 \text { if a die roll shows a six, and she wins } \$ 0.50} \\ {\text { otherwise. }}\end{array} $$

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Key Concepts

Expected Value

The expected value is a fundamental concept in probability and statistics that represents the long-run average outcome of a random process. It is calculated by multiplying each possible outcome by its corresponding probability and then summing up all these products. This concept is essential when making decisions under uncertainty, as it provides a single summary measure of the risk and reward associated with a random event.

Discrete Random Variable

A discrete random variable is a type of variable that can take on a countable number of distinct outcomes. In problems involving games or similar scenarios, outcomes are often defined for each possible event and linked to specific payoffs or losses. Understanding discrete random variables is crucial because it allows the use of probability mass functions to assign probabilities to each outcome, which are then used in the calculation of the expected value.

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