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.