# A casino offers a game in which a player places a \$3 bet on a 3 coming up on one roll of a six-sided die. If a 3 is rolled, the player keeps their \$3 and is paid \$12 by the house. If a number other than 3 is rolled, the house keeps the player's \$3. What is the expected value of this game to the player?

Using the equation for the expected value, it is found that the expected value of this game for the player is of -\$0.5.

The expected value is given by the sum of each outcome multiplied by it's probability.

In this problem:

• 1/6 probability of a 3 coming up, thus, 1/6 probability of the player earning \$12.
• 5/6 probability of a 3 not coming up, thus, 5/6 probability of the player losing \$3.

Then, the expected value is given by:

The expected value of this game to the player is of -\$0.5.

A similar problem is given at brainly.com/question/24855677

Expected Value = -1\$

Step-by-step explanation:

Expected Value: So, expected value is the very important concept of probability, from insurance to governments, from casinos to lotteries the concept of expected value is used. It is basically the expected gain or loss when you perform the task repeatedly.

So here’s the question statement:

Bet = 3\$

Bet is on: Number 3 of a 6 faced dice.

Total numbers on dice = 6 = Total number of outcomes

Bet is on how many numbers = 1 = Number of Favorable outcomes.

If you win: you will get:     12\$ = 3\$ (Bet amount) + 9\$ (outcome)

Outcome of winning = 9\$

Probability of winning = Favorable outcome divided by Total number of outcomes = 1/6 = 0.16666..

If you lose you will lose:   3\$ (Bet amount)

Outcome of losing = -3\$ ( - “minus” represents losing)

Probability of losing = Favorable outcome divided by Total number of outcomes = 5/6 = 0.8333…

So, expected value is calculated when you play this game repeatedly right?

Formula to calculate Expected Value:

Expected Value = (Outcome of Winning) x (Probability of Winning) + (Outcome of Losing) x (Probability of Losing)

So, we have all these variables. Now just put values into the equation of expected value.

Expected Value =  (9\$) x (1/6) + (-3\$) x (5/6)

Expected Value = -1\$

It means, every time you play the game you are expected to lose 1\$.

## Related Questions

A gas station sells three types of gas: regular for \$3.00 a gallon, performance plus for \$3.20 a gallon, and premium for \$3.40 a gallon. on a particular day 3700 gallons of gas were sold for a total of \$11,620. two times as many gallons of regular as premium gas were sold. how many gallons of each type of gas were sold that day?

A gas station sells three types of gas: Regular for \$2.90 a gallon, Performance Plus for \$3.05 a gallon, and Premium for \$3.20 a gallon. On a particular ... for \$3.20 a gallon. On a particular day 5000 gallons of gas were sold for a total of \$14,920. Three times as many gallons of Regular asPremium gas were sold.

Gale found out that the wave pool has a money-saving deal: if more than 4 people attend, the tickets are discounted from \$16.75 each to \$12.25 each. Calculate to determine how much 6 tickets to the wave pool will cost.

73.50

Step-by-step explanation:

12.25 times 6

I'm guessing 12.25 times 6

What is the slope and y intercept of x +7y = -7

X + 7y = -7
7y = -x -7
y = -1/7y - 1

slope = -1/7

y intercept = -1
Solve for y.

x + 7y = -7

7y = -x - 7

y = (-1/7)x - 1

slope = -1/7
y-intercept = -1

A family travels, by plane, five hundred miles from their city to a beach town. Then they take a taxi from the airport to the hotel at the beach. When they ask the driver how far the airport is from the hotel, he tells them twenty kilometers. What is the approximate total distance, in miles, the family traveled? Recall that 1 kilometer is about 0.62 miles. 330 miles