# CSE 321 Assignment #7

Spring 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:

- Section 4.5, Problems 28, 36.
- 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.)
- What is the probability that they will roll a double on their first
turn?
- 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?
- What is the overall expected number of steps they will move on their
first turn?
- What is the probability that they will roll doubles at least twice
in a row?
- What is the probability that they will roll doubles all three times
and therefore be sent to jail by their third roll?
- 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?
- (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?

- Section 6.1, Problems 4, 6, 14.
- Section 6.1, Problem 36 (You'll need induction for this one.)
- Section 6.3, Problem 8, 10.
- (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?