COS 341, October 1, 1997Handout Number 6
Homework Set 3
Reading Assignments Read Chapter 6.
Written Assignments Do exercises 5, 10, 19, 27 and 29 in Section 5.7.
Special Problem 1 (to be counted as 1 exercise) Let n>0. Evaluate
Your answer should be a closed-form expression.
Special Problem 2 (to be counted as
2 exercises) In the Math Casino Problem, suppose 
where s>0 is an
integer. The new rule is that a random 
will be
a winner for you if 
divides n.
What is p, the probability that a random n is a winner?
Give the answer as a closed-form expression involving s.
Special Problem 3 (to be counted as
2 exercises) In the National Basketball Association
finals, the format is for the two teams to play a best-of-seven
series. That is, the series stops whenever one team has accumulated
4 wins. Assume that the outcome of each game is
like a random fair coin toss, i.e. each team has a
50% chance of winning that game, independent of
what has happened so far in the series. Questions:
(a) What is the probability of a series going into
the seventh game?
(b) Let n be any positive integer. What is the probability
of a best-of-n series going into
the n-th game? (We again assume that the outcome of each game is
like a random fair coin toss.)