Expected Value

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.

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 winning $6 with a probability of 12/52 and $30 with a probability of 4/52?

Back

EV = (6 * 12/52) + (30 * 4/52) + (0 * 26/52) = $4.57.

Tags

CCSS.HSS.MD.A.2

Front

In a community where 20% have 1 child, 53% have 2 children, and 27% have 3 children, how do you find the expected number of children?

Back

EV = (1 * 0.20) + (2 * 0.53) + (3 * 0.27) = 2.07.

Tags

CCSS.HSS.MD.A.2

Front

What is the Expected Value of a game where rolling green wins $2, blue wins $6, and red loses?

Back

EV = (2 * 2/6) + (6 * 1/6) - (2 * 3/6) = -$0.33.

Tags

CCSS.HSS.MD.B.5A

Front

How do you determine if you expect to win or lose in a raffle with a total prize of $150, $50, and five $20 prizes?

Back

Calculate the total expected winnings and subtract the cost of the ticket. EV = (150/500) + (50/500) + (5*20/500) - 2 = -$1.40.

Tags

CCSS.HSS.MD.B.5A

Front

What is the Expected Value of a lottery ticket costing $7 with a prize of $800 and 1000 tickets?

Back

EV = (800/1000) - 7 = -$6.20.

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 when participating in that game or event.

Tags

CCSS.HSS.MD.B.5B

Front

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

Back

The probability of drawing a face card is 12/52 or 3/13.

Tags

CCSS.7.SP.C.7B

Front

What is the probability of winning nothing when drawing a card from a deck?

Back

The probability of winning nothing (drawing a non-face, non-ace card) is 26/52 or 1/2.

Tags

CCSS.7.SP.C.7B