Question
One: Players
start the game of monopoly from Go and throw two dice. The sum of
the two dice rolls ranges from 2 to 12. List all squares that the
player may land on after one roll of the two dice. What are the likelihoods
of landing on each property after one roll of the two dice?
For a discussion of question one go to the following post:
Question
Two: Each
turn of monopoly starts with a roll of two dice. If the player
rolls doubles (the same value on each dice) the person rolls again.
If the player rolls three doubles in a row the person goes directly to
jail. The player who rolls three doubles in a row does not get to
buy a property or use a community chest or chance card.
The
monopoly turn ends after the first roll of the dice if the dice roll is not
doubles and after the third roll of the dice regardless of the dice roll
outcomes.
The Chance
Square exists seven squares away from GO. What is the probability that a
player starts as Go and lands on Chance on the first turn of the game?
For a discussion of question two go to the following post:
Question Three: Sally owns
electric company but does not own waterworks. Mark lands on
electric company. The rent on electric company is 4 times the sum
of two dice throws. What is the value of each possible amount that Mark will
owe Sally and the probability of that outcome? What is most likely amount
that Mark will owe Sally? What is the expected amount that Mark
will owe Sally?
Sally buys waterworks and Mark lands on electric
company again. The rent is now 10 times the sum of the two dice
rolls. What is the most likely amount that Mark will owe
Sally? What is the expected amount?
In these two problems the most likely amount owed
and the expected amount owed are equal. Is this always the
case? Why or why not?
What is the most likely payoff from landing on
electric company and the expected rent from landing on electric company if the
rent is the square of the sum of the two dice rolls in dollars?
For a discussion of question three go to the
following post:
Question
Four: What is
the skewness of rent from electric company when rent is $4.00 times the sum of
the values from two dice rolls?
Would the
skewness number change if rent is $10 times the sum of the two dice rolls?
What is
the skewness number if rent was equal to the square of the sum of the two dice
rolls?
For a
discussion of question four go to the following post.
Question
Five: What is
the probability that a person starts the game by throwing doubles on the first
throw and then throws a second time and lands on Pennsylvania
Railroad? (Pennsylvania Railroad is the railroad that is 15 squares
away from Go, the opening square.)
For a
discussion of question five go here:
Question
Six: A person
starts on Kentucky Avenue and throws the dice once. (We will
consider ramifications of doubles in a future post but for now let’s assume the
person does NOT go again if he throws doubles.)
The
player’s opponent owns all three yellow properties  Atlantic, Ventnor,
and Marvin Gardens. The rents at these three properties for
two houses and for three houses are presented below.
Rent at Atlantic, Ventor, and Marvin Gardens






Two Houses

Three Houses

Atlantic

330

800

Ventor

330

800

Marvin Gardens

360

850

What is
the likelihood that the person will not land on any of these three properties
after one throw of the two dice?
What is
the most likely outcome after one throw of the two dice?
What are
the expected value, standard deviation, and skewness of rents given two houses
and given three houses?
For a
discussion of question six go to the following place.
Question: A person rolls the two
dice from Go. After the roll of the two dice the player moves the
dice back to Go and goes again. What is the probability that at
least one of the two rolls lands the person on chance, the square that is seven
squares away from Go?
Hint: The answer is NOT the
sum of the probabilities from the first try and the second try. Think
of the probability of getting two heads on two coin tosses. The
answer is NOT the sum of the probabilities for the two coin tosses.
I hope that you and your students benefit from these
problems.
Very nice questions. Thank you for sharing.
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