Expected Value

Front

What is Expected Value?

Back

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

Front

How do you calculate Expected Value?

Back

To calculate the Expected Value, multiply each possible outcome by its probability and sum all these products: EV = Σ (X * P(X)).

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

EV = (50 * 0.1) + (20 * 0.3) + (5 * 0.6) = 5 + 6 + 3 = 14.

Front

What is the probability of rolling two dice and both landing on 6?

Back

The probability of rolling two sixes is 1/36.

Front

If you win $25 for rolling two sixes and lose $1 otherwise, what is the Expected Value of this game?

Back

EV = (1/36 * 25) + (35/36 * -1) = 0.6944 - 0.9722 = -0.2778.

Front

In a raffle with 500 tickets sold at $2 each, what is the total revenue generated?

Back

Total revenue = 500 tickets * $2 = $1000.

Front

What is the Expected Value of winning in a raffle with a $100 prize, a $50 prize, and five $20 prizes?

Back

EV = (1/500 * 100) + (1/500 * 50) + (5/500 * 20) = 0.2 + 0.1 + 0.2 = 0.5.

Front

If you spend $2 on a raffle ticket, what is the Expected Loss?

Back

Expected Loss = Cost of ticket - Expected Value of winnings = 2 - 0.5 = 1.5.

Front

What is the Expected Value of picking a face card ($5) or an ace ($30 + $60 for ace of hearts)?

Back

EV = (12/52 * 5) + (4/52 * 30) + (1/52 * 60) = 1.1538 + 2.3077 + 1.1538 = 4.6153.

Front

What is the Expected Value of betting $6 on red in roulette?

Back

EV = (18/38 * 6) + (20/38 * -6) = 2.8421 - 3.1579 = -0.3158.