# CSE 321 Assignment #7Spring 2001

### Due: Friday, May 18, 2001 at the beginning of class.

Reading assignment: Read the text, Discrete Mathematics and Its Applications, sections 6.1-6.4.

The following problems are from the Fourth Edition of the text:

1. Section 4.5, Problems 28, 36.

2. In a player's turn during the game of Monopoly, the player will roll a pair of dice to determine the number of steps they will move (which is the sum of the values on the two dice). If the player rolls a double (the two numbers match) then they get to take another turn immediately, otherwise the next player gets to move. The same thing happens if they roll doubles a second time. If they roll three doubles in a row they must move directly to "jail" and the next player gets to move. (In answering the following questions please ignore the fact that in the real game of Monopoly, by moving to certain locations, one may be sent to other locations on the board or one's turns may be halted prematurely by being bankrupted.)

1. What is the probability that they will roll a double on their first turn?

2. What is the expected number of steps they will move on their first turn, given that they rolled doubles? given that they didn't roll doubles?

3. What is the overall expected number of steps they will move on their first turn?

4. What is the probability that they will roll doubles at least twice in a row?

5. What is the probability that they will roll doubles all three times and therefore be sent to jail by their third roll?

6. Suppose that the rules were changed so that players simply stopped rolling after their second double. What would be the expected total number of steps they would have moved by the time the next player got to move if we made this change to the rules?

7. (Bonus) What is the expected number of steps they will move given that they do not get sent to jail by rolling doubles three times in a row?

3. Section 6.1, Problems 4, 6, 14.

4. Section 6.1, Problem 36 (You'll need induction for this one.)

5. Section 6.3, Problem 8, 10.

6. (Bonus) A coin is flipped repeatedly. What is the expected number of coin flips before a fair coin lands heads 3 times in a row?