Expected Value Spiral Review

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.

Front

How do you calculate Expected Value?

Back

To calculate Expected Value, multiply each possible outcome by its probability and sum all these products. Formula: EV = Σ (Outcome × Probability).

Front

What is the Expected Value of a game where you lose $2 for a red roll, gain $2 for a green roll, and gain $5 for a blue roll with respective probabilities?

Back

EV = (1/2 * -2) + (1/3 * 2) + (1/6 * 5) = -0.50.

Front

In a lottery with 1000 tickets, how do you find the Expected Value of buying a ticket for $6 with a prize of $800?

Back

EV = (1/1000 * 800) - 6 = -5.20.

Front

What does a negative Expected Value indicate?

Back

A negative Expected Value indicates that, on average, you will lose money if you play the game or participate in the event repeatedly.

Front

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

Back

EV = (1/6)*(1 + 2 + 3 + 4 + 5 + 6) = 3.5.

Front

What is the mean (μ) in probability and statistics?

Back

The mean (μ) is the average of a set of values, calculated by summing all values and dividing by the number of values.

Front

How do you find the standard deviation (σ) of a probability distribution?

Back

Standard deviation (σ) measures the dispersion of a set of values. It is calculated as the square root of the variance.

Front

What is the relationship between Expected Value and risk?

Back

Expected Value helps assess the risk of a decision by providing a quantitative measure of potential outcomes and their likelihoods.

Front

What is a fair game in terms of Expected Value?

Back

A fair game is one where the Expected Value is zero, meaning that neither the player nor the house has an advantage.