Master

Word Problems: Expected Value

Master word problems: expected value with interactive lessons and practice problems! Designed for students like you!

Learn

Get the basics

Practice

Apply your skills

Master

Achieve excellence

Word Problems: Expected Value

Study Guide

Key Definition

Expected Value is a calculation used to find the average outcome of a probability experiment, given by $\sum (\text{value} \times \text{probability})$.

Important Notes

Expected Value helps in decision making under uncertainty.
If $\text{Expected Value} > 0$, the investment is likely beneficial.
Consider risk factors like probability of adverse conditions.
Expected Value does not guarantee results but indicates likely outcomes.
In finance, it's used for predicting investment returns.

Mathematical Notation

$+$ represents addition

$-$ represents subtraction

$\times$ represents multiplication

$\div$ represents division

$\sum$ symbolizes summation

Remember to use proper notation when solving problems

Why It Works

Expected Value works because it averages out all possible outcomes, weighted by their probabilities, to provide a single measure of central tendency for the potential outcomes.

Remember

Expected Value formula: $\text{EV} = \sum (\text{value} \times \text{probability})$

Quick Reference

Formula:$\text{EV} = \sum (\text{value} \times \text{probability})$

Understanding Word Problems: Expected Value

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Simple explanation with $\text{EV} = \sum (\text{value} \times \text{probability})$

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the Expected Value if you have a 50% chance to win $\$100$ and 50% chance to lose $\$50$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

A game has a $20\%$ chance of winning $\$50$ and an $80\%$ chance of losing $\$10$. Calculate the Expected Value.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

You invest in a project with $30\%$ chance of gaining $\$200$ and $70\%$ chance of losing $\$50$. Is this a good investment?

Challenge Quiz

Single Choice Quiz

Advanced

A raffle ticket costs $\$10$. There's a $5\%$ chance to win $\$200$ and a $95\%$ chance to win nothing. What is the Expected Value?

Recap

Watch & Learn

Review key concepts and takeaways