Question

Your friend asks you to play a gambling game. If you give her $1,
you get to roll two dice. If you get a total of 11 or 12, she will
give you a $5 bill. If your total is 7 she will give back your $1.
Otherwise she keeps your $1. Let X be your overall gain after one
round.

a) Construct the probability distributio table for X.

b) Compute E(X).

c) If you started with $1000, how much money would you expect
to have after playing this game 1000 times?

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?

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...

A game consists of rolling two dice. The game costs $2 to play.
You roll a two dice. If the outcome totals 9 you get $10.
Otherwise, you lose your $2. Should you play the game? Explain
using probability.

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?

Your friend wants to play a game with a pair of dice. You win if
the sum of the top faces is 5, 6, 7, or 8. The winner pays the
loser $1 each game. Should you play?

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:...

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...

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...

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:...

Suppose you play a betting game with a friend. You are to roll
two fair 6-sided dice. He says that if you roll a 7 or 11, he will
pay you $100. However, if you roll anything else, you owe him $20.
Let x denote the discrete random variable that represents the
amount you are paid, i.e., x = $100, and the amount you have to
pay, i.e., x = −$20.
Create a table for the probability distribution of x....

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