Question

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, or five on the two dice you win $2. If it costs $5 to play the game, is it a fair game?

Answer #1

You pay $1 to play a game. The game consists of rolling a pair
of dice. If you observe a sum of 7 or 11 you receive $4. If not,
you receive nothing. Compute the expected value and standard
deviation for this game?

You pay $1 to play a game. The game consists of rolling a pair
of dice. If you observe a sum of 7 or 11 you receive $4. If not,
you receive nothing. Compute the expected value and standard
deviation for this game?

. 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.

Please follow the comment.
2. Roll two fair dice repeatedly. If the sum is ≥ 10, then you
win.
(a) What is the probability that you start by winning 3 times in
a row?
(b)What is the probability that after rolling the pair of dice 5
times you win exactly 3 times?
(c) What is the probability that the first time you win is
before the tenth roll (of the pair), but after the fifth?

For the following questions, find the
probability using a standard 6-sided die or two 6-sided dice. Write
your answer as a fraction or with a colon in lowest terms.
Rolling a single die, what is the probability of rolling an
even number?
Rolling a single die, what is the probability of rolling a
5?
Rolling a single die, what is the probability of rolling a
7?
Rolling a single die, what is the probability of rolling a
number less than...

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?

The following game is played in a casino. The participant would
roll two fair dice and if they sum to 8 or higher, the participant
wins 4$ otherwise they lose 3$. What is the expected payout the
casino will make as each game is played?

If the theoretical probability of rolling a sum of five with two
fair dice is 1/9 and a student answers the probability is 1/11 can
you explain what is wrong with students approach?

Question:
Q1) An experiment consists of rolling two fair dice and
recording the outcome as an ordered pair: (#1st die, #2nd die).
a. Find the sample space S of the experiment (list each
outcome).
b. Let A be the event that the sum of the dice is 4. Find A and
P(A)
c.Let B be the event that at least one of the dice lands on 3.
Find B and P(B).
d. Find A n B and P(A n B)...

B: A game is played with two strange dice.
Dice A: Five sides display "4" and one side displays "1"
Dice B: Two sides display "5" and four sides display "3"
In StatCrunch, create a probability model for the total sum you
get when you roll the two dice. Then use StatCrunch to find the
mean and standard deviation of your model. Take a screen shot that
displays BOTH items and submit it.

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