expected value practice

Front

What is the expected value?

Back

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

Front

What is the formula for calculating expected value?

Back

Expected Value (EV) = Σ (Probability of Outcome × Value of Outcome) for all outcomes.

Front

If you roll a die, what is the expected value of rolling a 1?

Back

The expected value of rolling a 1 is 1/6, since there is a 1 in 6 chance of rolling a 1.

Front

What is the expected value of a game where you win $10 with a probability of 0.2 and lose $5 with a probability of 0.8?

Back

EV = (0.2 × 10) + (0.8 × -5) = 2 - 4 = -2.

Front

How do you find the expected value of a spinner with equal sections?

Back

For a spinner with equal sections, the expected value is the average of the values on the spinner.

Front

What is the expected value of a raffle ticket if the prizes are $100, $50, and $20 with 500 tickets sold?

Back

EV = (1/500 × 100) + (1/500 × 50) + (5/500 × 20) = 0.20 + 0.10 + 0.20 = 0.50.

Front

What does a negative expected value indicate?

Back

A negative expected value indicates that, on average, you will lose money over time if you play the game repeatedly.

Front

What is the expected value of rolling a standard die?

Back

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

Front

In a game where you win $20 with a probability of 0.1 and lose $10 with a probability of 0.9, what is the expected value?

Back

EV = (0.1 × 20) + (0.9 × -10) = 2 - 9 = -7.

Front

What is the expected value of a spinner with sections labeled 1, 2, 3, and 4?

Back

EV = (1/4 × 1) + (1/4 × 2) + (1/4 × 3) + (1/4 × 4) = 2.5.