Expected Value

Front

What is Expected Value?

Back

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.

Tags

CCSS.HSS.MD.A.2

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).

Tags

CCSS.HSS.MD.A.2

Front

What is the Expected Value of rolling a die where you win $12 for a six, $6 for a one, and $0 for any other number?

Back

$3

Tags

CCSS.HSS.MD.B.5A

Front

In a game where you win $200 for two yellow marbles, $50 for one yellow, and $100 for two red, how do you find the Expected Value?

Back

Calculate the probability of each outcome, multiply by the winnings, and sum them up. The Expected Value is $20.

Tags

CCSS.HSS.MD.B.5A

Front

What is the probability of picking a face card from a standard deck of cards?

Back

There are 12 face cards in a deck of 52 cards, so the probability is 12/52 or 3/13.

Tags

CCSS.7.SP.C.7B

Front

If you lose $5 for picking a non-face card and win $10 for a face card, what is the Expected Value of this game?

Back

The Expected Value is -$1.50.

Tags

CCSS.HSS.MD.B.5A

Front

What is the Expected Value of rolling two dice and winning $10 for a sum of 7, $5 for a sum of 6 or 8, and $0 otherwise?

Back

The most reasonable amount to pay to play this game is $2.

Tags

CCSS.HSS.MD.B.5A

Front

What does it mean if the Expected Value is positive?

Back

A positive Expected Value indicates a favorable game or investment, suggesting that, on average, you can expect to win.

Tags

CCSS.HSS.MD.B.5B

Front

What does it mean if the Expected Value is negative?

Back

A negative Expected Value indicates an unfavorable game or investment, suggesting that, on average, you can expect to lose.

Tags

CCSS.HSS.MD.B.5B

Front

How does the law of large numbers relate to Expected Value?

Back

The law of large numbers states that as the number of trials increases, the sample mean will converge to the Expected Value.

Tags

CCSS.6.SP.A.3