Question

You are playing another dice game where you roll just one
die--this time, you *lose* a point if you roll a 1. You are
going to roll the die 60 times. Use that information to answer the
remaining questions.

**A. What are the values of p and q? (Hint: notice this is
binomial data, where p is the probability of losing a point and q
is the probability of not losing a point.) p =
and q =**

B. **What is the average number of points you would expect
to lose (rolling the die 60 times)?**

C. Although you expect to lose a certain number of points on
average, a typical game of 60 rolls will vary in how many points
are lost. **In other words, what is the standard deviation of
this distribution?**

**D. Your unlucky friend Unlucky Louis just played the
game and lost 17 points! Just how unlucky is Unlucky Louis? In
other words, what is p(X≥17)? (Hint: remember real intervals--this
question is asking about the probability of losing 17 or
more points.)**

**First, what is the Unlucky Louis' Z-score?**

**E. Finally--so how unlucky is he? That is, what is the
probability of the Z-score you found for the last question? (Hint:
make sure to draw it and pay attention to whether it's the tail or
the body.)**

Answer #1

1. Game of rolling dice
a. Roll a fair die once. What is the sample space? What is the
probability to get “six”? What is the probability to get “six” or
“five”?
b. Roll a fair die 10 times. What is the probability to get
“six” twice? What is the probability to get six at
least twice?
c. Roll a fair die 10 times. What is the expected value and
variance of getting “six”?
d. If you roll the die...

Someone offers you a game of unbiased die roll, where you win
153 USD on 1, and lose 181 USD on anything other than 1. What is
the expected value of one roll?

PROBLEM #2
Suppose you play a game in which a fair 6 sided die is rolled
once. If the outcome of the roll (the number of dots on the side
facing upward) is less than or equal to 4, you are paid as many
dollars as the number you have rolled. Otherwise, you lose as many
dollars as the number you have rolled.
Let X be the profit from the game (or the amount of money won or
lost per...

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:...

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:...

If you were to roll 3 die, how many even numbers should you
expect to show up? Perform this experiment 16 times where you roll
3 die and record the number of evens that show up in each
trial.
Then answer the following questions:
1) How does this game satisfy a binomial distribution?
2) Determine the probability of each outcome based on the
results of your experiment and then determine what the actual
probability should be using the binomial probability...

Bunco is a group dice game that requires no skill. The objective
of the game is to accumulate points by rolling certain
combinations. The game is played with three dice, but we will
consider a simpler version involving only two dice. How do you play
two dice Bunco? There are six rounds, one for each of the possible
outcomes in a die, namely the numbers one through six. Going
clockwise, players take turns rolling two dice trying to score
points....

imagine a simple game where you roll two dice at the same
time.Your"score"for the round is equal to the higher value of the
two dice. So, if you tolled a 1 and 4, your score for that round
would be 4. If you rolled two 4s, your score for that round would
also be 4.
Simulate 1,000,000 round of this game.
1) What is the average score for all 1,000,000 rounds of your
simulation?
2? In your simulation, what percent...

Suppose that you are offered the following "deal." You roll a
six sided die. If you roll a 6, you win $17. If you roll a 4 or 5,
you win $2. Otherwise, you pay $10.
a. Complete the PDF Table. List the X values, where X is the
profit, from smallest to largest. Round to 4 decimal places where
appropriate.
Probability Distribution Table
X
P(X)
b. Find the expected profit. $ (Round to the nearest cent)
c. Interpret the...

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