Expected Value and Fair Games

Front

What is Expected Value?

Back

The expected value is a calculated average of all possible outcomes of a random variable, weighted by their probabilities.

Front

How do you calculate Expected Value?

Back

Expected Value (EV) = Σ (X * P(X)), where X is the outcome and P(X) is the probability of that outcome.

Front

What does a negative Expected Value indicate?

Back

It indicates that a player can expect to lose more money than they win in the long run.

Front

What is a Fair Game?

Back

A fair game is one where the expected value is zero, meaning players neither gain nor lose money on average.

Front

What is the Expected Value of a random variable with outcomes 50, 20, and 5 with probabilities 0.1, 0.3, and 0.6 respectively?

Back

14

Front

What does it mean if a game has a high Expected Value?

Back

It means that, on average, players can expect to win more than they lose.

Front

What is the Expected Value of a spinner with outcomes 1, 2, 3, 4, 5, and 6, each with equal probability?

Back

The Expected Value is 3.5.

Front

If a lottery ticket costs $2 and the prize is $10 with a probability of winning 0.1, what is the Expected Value of the ticket?

Back

EV = (0.1 * 10) - (0.9 * 2) = -0.8.

Front

What is the relationship between Expected Value and risk?

Back

Higher expected values often come with higher risks, while lower expected values may indicate safer bets.

Front

What is the Expected Value of rolling a fair six-sided die?

Back

The Expected Value is 3.5.