CHAPTER 11 - PROBLEMS FOR WRITING AND DISCUSSION
1. When throwing two fair dice, the possible sums are 2 through 12. There are 11
possible sums; thus the probability of tossing a sum of 2 is 1/11. Do you agree?
Discuss.
2. An octahedron is a three-dimensional shape with eight sides that are equilateral
triangles. This shape is used as a die in some games, such as "Dungeons and
Dragons," because all eight sides come up with equal probability. Assuming the sides
are numbered 1 through 8, and a person throws two octahedral dice, what are the
possible sums? Which sum has the highest probability? Explain.
3. To play the Ohio Lottery, a person has to choose six different numbers from 1 to 50.
Once a week, the six winning numbers are selected (without replacement) from a
drum that contains 50 balls, each with a number from 1 to 50. When the Ohio Lottery
Jackpot reaches $13,000,000, many people purchase $1 tickets to win. If more than
one person selects the winning combination, all winners have to split the pot. If no
one picks the winning numbers, the $13,000,000 gets added to the Jackpot for the
following week. If 2,000,000 tickets are sold, what is the probability of any collection
of six different numbers turning up? What conclusions can you draw about the
purchase of a lottery ticket?
4. Irene is playing a board game, and she is only five squares away from Home. To
move forward, she tosses a coin; if she gets heads, she moves forward 1 square and if
she gets tails, she moves forward 2 squares. It will take her at least three turns (coin
tosses) to get to Home. What is the probability that it will take her four turns?
Explain. (Hint: Make a tree diagram that takes into account all the possible ways
Irene could get Home.)
5. Explain how you would go about using a simulation with a coin, a die, or a deck of
cards to verify your answer to Problem 4. Then do the simulation. About how many
trials would it take to conclude reasonably that you had verified, or disproved, your
calculations for Problem 4?
6. In the Focus On at the beginning of chapter 11, it was stated that you might have had
any of 8,388,608 different sets of characteristics when you were conceived. How did
the author determine that number? Explain.
7. It was also stated in the Focus On that if you used random guessing on a true/false
test with 10 items, your chance of guessing 70% or more of the answers correctly was
about 0.17. Explain how the author determined this answer.