Question

You pay $20 to play a game of chance. You will win $80 if you spin a “7”, and you will win $30 if you spin an even number. All other outcomes you will make you lose. (Board numbers are from 1-8)

a. Find the expectation of this game.

b. Is it a fair game? Explain.

c. How much must be charged for the game to be fair?

Answer #1

You play a gambling game with a friend in which you roll a die.
If a 1 or 2 comes up, you win $8. How much should you lose on any
other outcome in order to make this a fair game?

One plays a game where you spin a spinner with the numbers 1
through 10 on it in equal parts. It costs $7 to
play. If you spin a two then you win $25. If
you spin an odd number then you win $10. You decide to
play the game once. What are your expected winnings?

On the average, how much would you expect to win by playing the
following game? A 50% chance to win $2000, a 30% chance to lose
$1000, and a 20% chance to lose $2000.
a) $1000 gain
b) $300 loss
c) $400 loss
d) $300 gain
On the average, how much would you expect to win by playing the
following game? A 60% chance to win $3000 and a 40% chance to lose
$1000.
a) $1800 gain
b) $400 loss...

In a particular carnival game you pay $10 to play and select two
cards. If both cards are face
cards you win $200. If the probability of selecting two face cards
is .0498 what is
the expected value of the game to the player?
If the game is played 1000 times how much would you expect to
win/lose?

The game requires $5 to play, once the player is admitted, he
or she has the opportunity to take a chance with luck and pick from
the bag. If the player receives a M&M, the player loses. If the
player wins a Reese’s Pieces candy, the player wins. If the player
wins they may roll a dice for a second turn, if the die rolls on a
even number, they may pick from the bag once again with no extra...

There is a game at the local carnival where you pay $1 for a
chance to draw one card from a standard deck. If you draw an ace,
you win $3.50 and if you draw a face card, you win $2. Otherwise
you don’t win anything. Find the expected value to you for this
game. Explain why it is or is not a good idea to play this
game.

You are trying to decide whether to play a carnival game that
costs $1.50 to play. The game consists of rolling 3 fair dice. If
the number 1 comes up at all, you get your money back, and get $1
for each time it comes up. So for example if it came up twice, your
profit would be $2. The table below gives the probability of each
value for the random variable X, where:
X = profit from playing the...

A game of chance involves rolling a 15-sided die once. If a
number from 1 to 3 comes up, you win 2 dollars. If the number 4 or
5 comes up, you win 8 dollars. If any other number comes up, you
lose. If it costs 5 dollars to play, what is your expected net
winnings?

I propose to you a game. You roll 2 dice. If the sum of the
numbers showing is either 6, or 7, or 8, I win. If it is 2, 3, 4,
5, 9, 10, 11, 12, you win. Since you have lots more possible
winning combinations than I do, the rules are that you pay me $2.00
when I win and I pay you $1.00 when you win. If we play this game
30 times, how much do you...

(9 pts) In a casino game, you pay $5 to play. You draw a card
from a standard deck. If you draw any card ace (worth 1) through
10, you receive twice the number of dollars as the card’s number
(so if you draw a 7, you get $14). You lose if you draw a face
card. Make the probability distribution for this game, find the
expected value of a bet, and decide if you should play.

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