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.

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. EV = Σ (Outcome × Probability).

Tags

CCSS.HSS.MD.A.2

Front

What is the Expected Value of a fair die roll when winning $3 for rolling a 2 or 4 and losing $1 for rolling any other number?

Back

$0.00

Tags

CCSS.HSS.MD.B.5A

Front

What is the Expected Value of a probability distribution with outcomes 85, 83.2, 87.1, and 84.4?

Back

84.4

Tags

CCSS.HSS.MD.A.2

Front

If a raffle ticket costs $2 and the total prizes are $100, $50, and five $20 gift cards, what is the Expected Value of buying a ticket?

Back

You lose an average of $1.50.

Tags

CCSS.HSS.MD.B.5A

Front

What is the Expected Value of the number of cars in a randomly chosen American household?

Back

1.75

Tags

CCSS.HSS.MD.A.2

Front

If you roll two dice and win $10 for a sum of 7, $5 for a sum of 6 or 8, and $0 otherwise, what is a reasonable amount to pay to play?

Back

$2

Tags

CCSS.HSS.MD.B.5A

Front

What does a negative Expected Value indicate?

Back

A negative Expected Value indicates that, on average, a player can expect to lose money over time.

Tags

CCSS.HSS.MD.B.5B

Front

What is the significance of Expected Value in decision-making?

Back

Expected Value helps in making informed decisions by evaluating the potential outcomes and their likelihoods.

Tags

CCSS.HSS.MD.B.5B

Front

What is a fair game in terms of Expected Value?

Back

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

Tags

CCSS.HSS.MD.B.5B