Expected Value and Fair Games

Front

What is Expected Value?

Back

Expected Value (EV) is a calculated average of all possible outcomes of a random event, weighted by their probabilities. It represents the long-term average if the event were repeated many times.

Tags

CCSS.HSS.MD.A.2

Front

How is Expected Value calculated?

Back

Expected Value is calculated by multiplying each possible outcome by its probability and summing all these products.

Tags

CCSS.HSS.MD.A.2

Front

What does a positive Expected Value indicate?

Back

A positive Expected Value indicates that, on average, a player can expect to win money over time.

Tags

CCSS.HSS.MD.B.5B

Front

What does a negative Expected Value indicate?

Back

A negative Expected Value indicates that, on average, a player can expect to lose money over time.

Tags

CCSS.HSS.MD.B.5B

Front

What is the Expected Value of a fair game?

Back

In a fair game, the Expected Value is zero, meaning players neither gain nor lose money in the long run.

Tags

CCSS.HSS.MD.A.2

Front

What is the Expected Value in a lottery game?

Back

The Expected Value in a lottery game is the average amount of money a player can expect to win or lose from a single ticket.

Tags

CCSS.HSS.MD.A.2

Front

What is a fair game?

Back

A fair game is one where the Expected Value is zero, meaning the average outcome is neither a win nor a loss.

Tags

CCSS.HSS.MD.B.5B

Front

How does probability affect Expected Value?

Back

Probability directly influences Expected Value; higher probabilities of winning increase the Expected Value.

Tags

CCSS.HSS.MD.A.2

Front

What is the formula for Expected Value?

Back

The formula for Expected Value is EV = Σ (Outcome × Probability) for all possible outcomes.

Tags

CCSS.HSS.MD.A.2

Front

What is an example of calculating Expected Value?

Back

If a game has outcomes of $10 (with a probability of 0.1) and $0 (with a probability of 0.9), the EV = (10 * 0.1) + (0 * 0.9) = $1.

Tags

CCSS.HSS.MD.A.2