Question

. A
dice game is played as follows: you pay one dollar to play, then
you roll a fair six-sided die. If you roll a six, you win three
dollars. Someone claims to have won a thousand dollars playing this
game nine thousand times. How unlikely is this? Find an upper bound
for the probability that a person playing this game will win at
least a thousand dollars.

Answer #1

please like if it helps

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?

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...

(Need solution for part b) You are offered to play the following
game. You roll a fair 6-sided die once and observe the result which
is shown by the random variable X. At this point, you can stop the
game and win X dollars. Or, you can also choose to discard the X
dollars you win in the first roll, and roll the die for a second
time to observe the value Y . In this case, you will win...

Probability. Read prompt and answer 3 questions.
To play a game, you have a bag containing:
• 30 fair six-sided dice, with faces
{1,2,3,4,5,6}.
• 17 fair eight-sided dice (faces {1,2,3,4,5,6,7,8})
• and 3 fair twenty-sided dice (faces {1,2,3,...,19,20})
Call these 3 classes of die "Six", "Eight" and "Twenty" (or S,
E, and T, for short).
Please show your work and answer the following questions:
Part A: You roll your die one time. What is the
probability of the event ?7R7,...

Over Christmas break, I was at an Elk Lodge that offered the
following dice game that cost $1 to play. You roll 5 six-sided dice
and win the money in the pot if all 5 dice are the same (e.g., all
ones). When I was there, the pot was at $156.
a) Based upon probability, should I have played?
b) Based upon probability, what is the minimum amount of money
required in the pot for me to play?

1. Answer the following questions on probability
distributions:
a) A game is played by rolling two dice. If the sum of the dice
is either 2 or 11 then you win $2. If the sum is a 5, then you win
$1. All other sums you win zero. If the cost of the game is 75
cents, is the game fair?
b)A game consists of rolling a pair of dice 10 times. For each
sum that equals either three, four,...

A game is played. One dollar is bet and 3 dice are rolled. If
the sum of the eyes of the dice is smaller than 5, one wins 20
dollar otherwise one looses the 1 dollar.
Find the approximation of the distribution of the total wins
after 200 games. What is the Probabilty that the total win is
positive. Use the CLT and state why.

Suppose you are playing a game of chance. You pay $50 to play
by rolling a fair die one time, if you roll a 1 you will receive
$300, if you roll a 3 or a 6 you will receive $150, if you roll a
2, 4 or 5 you will receive nothing.
(6)
Find your (the player’s) expected value for this game of
chance.
Based on this expected value, do you think this would be...

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...

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?

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