Скачать или смотреть Introduction to expected value

*CORE CONCEPT:*
Expected value is a mathematical concept used to determine the average outcome of a game of chance by considering all possible results and their probabilities.

*TOPICS COVERED:*
When to use expected value to evaluate games of chance (B1)
How to calculate expected value using probabilities and outcomes (B1)
When to apply expected value for informed decision-making in simple games (B1)

*EXAMPLE SENTENCES:*
Example 1: You flip a coin. If it lands on heads, you win $10; if tails, you win $0. The expected value is (1/2 * 10) + (1/2 * 0) = 5.
Example 2: In a game, you roll a die. You win $6 if you roll a 6, and lose $2 otherwise. The expected value is (1/6 * 6) + (5/6 * -2) = 1 - 1.67 = -0.67.
Example 3: In a raffle, you buy a ticket for $5. You have a 1 in 50 chance to win $250. The expected value is (1/50 * 250) - 5 = 5 - 5 = 0.

*GRAMMAR RULES:*
Step 1 → Identify the possible outcomes of the game and their probabilities.
Step 2 → Multiply each outcome by its probability to find the weighted value.
Step 3 → Sum all the weighted values and subtract any costs to find the expected value.

*COMMON ERRORS:*
Wrong: Not considering all possible outcomes when calculating expected value. → Right: Ensure all outcomes are accounted for in your calculations.
Wrong: Forgetting to multiply the outcome by the probability. → Right: Always multiply the probability by the outcome before summing.
Wrong: Adding probabilities instead of multiplying by outcomes. → Right: Check your calculations to ensure you are adding weighted values correctly.

*STUDENT QUESTIONS:*
How do I calculate expected value?
When should I use expected value in games?
Is this expected value example correct?
What's the difference between expected value and actual outcome?

*KEY CONCEPTS:*
Expected value, probability, outcomes, decision-making, B1, games of chance.