Question

There are four dice with varying numbers on each face:

Die A. has 1 2 4 5 6 7

Die B. has 4 4 4 4 4 4

Die C. has 2 6 2 6 2 2

Die D. has 3 5 3 5 3 5

You and three friends play a game where you each roll one of the dice and the highest number wins.

You get first pick from the dice. Question: Which die should you choose in order to maximize your chance of winning?

Answer #1

If you roll a die, you get one of the following numbers: 1, 2,
3, 4, 5, 6. Each possibility occurs with equal probability of 1/6.
The expected value of a dice roll is E(D)= 3.5 and the variance of
a dice roll is Var(X) = 2.917.
a) Suppose you roll a die and then add 1 to the roll to get a
new random variable taking one of the following numbers:
2,3,4,5,6,7. What is the variance of this new...

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...

You and a friend are rolling a set of 6 dice. The game works
such that if a die shows the values 1, 2, or 3 you will get a point
for that die. Each die that shows 4, 5, or 6 your friend will get a
point for.
Construct a probability model for a single roll of the dice then
answer the following.
Step 1 of 5:
What is the probability you made 2 points?
Step 2 of 5:...

A game of chance involves rolling a standard, six-sided die. The
amount of money the player wins depends on the result of the die
roll:
* If the result is 1 or 2, the player wins
nothing;
* If the result is 3, 4, or 5, the player wins 8
dollars;
* If the result is 6, the player wins 42
dollars.
(Note: Your answer to the question below should be rounded to
three decimal places.)
If you play this...

You and a friend are rolling a set of 5 dice. The game works
such that if a die shows the values 1, 2, 3, or 4 you will get a
point for that die. Each die that shows 5 or 6 your friend will get
a point for. Construct a probability model for a single roll of the
dice then answer the following.
Step 1 of 5:
What is the probability you made 2 points?
Step 2 of 5:...

In a game, you roll two fair dice and observe the uppermost face
on each of the die. Let X1 be the number on the first die and X2 be
the number of the second die. Let Y = X1 - X2 denote your winnings
in dollars.
a. Find the probability distribution for Y .
b. Find the expected value for Y .
c. Refer to (b). Based on this result, does this seem like a
game you should play?

The following describes a dice game played at a carnival. The
game costs $5 to play. You roll the die once. If you roll a one or
a two, you get nothing. If you roll a three or a four, you get $4
back. If you roll a five you get your $5 back and if you roll a
six, you receive $12. What is your Expected Value? Should you play
the game?

You and a friend are rolling a set of 7 dice. The game works
such that if a die shows the values 1, 2, 3, or 4 you will get a
point for that die. Each die that shows 5 or 6 your friend will get
a point for.
Construct a probability model for a single roll of the dice then
answer the following.
A)What is the probability you made 2 points?
B)What is the probability that your friend will...

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...

My friend and I are playing a gambling game in which we each
roll a die. We then compare the numbers on the two dice to
determine the outcome. If my roll is larger, I win $1 and my friend
loses $1. If her roll is larger, I lose $1 and she wins $1. And if
our two rolls are equal, we both don’t win or lose any money.
(a) Write your answers as simplified fractions: What is the
chance...

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