where 
represent,
respectively, the door Monte chooses to hide the
Holidays,'' the door the contestant picks,
and the ``Donkey'' door Monte shows to the contestant.
Written Assignments Read Chapter 1, Chapter 3.
Written Assignments Do Exercises 3, 4, 7, 12, 22, 28 in Section 1.8.
Special Problem 1 (to be counted as 2 exercises) In class, we demonstrated that for the Monte-Hall Problem the switch'' strategy is better than the non-switch''. Give a precise mathematical description of the probability space, the event of winning a holiday in each strategy, and compute the probability for the event (for each strategy). (The answers should be 2/3 and 1/3 for the two strategies.)
Hint One can take as Universe the set of all
triplets where represent,
respectively, the door Monte chooses to hide the
Holidays,'' the door the contestant picks,
and the ``Donkey'' door Monte shows to the contestant.
Special Problem 2 (to be counted as
2 exercises; you may use the computer if you wish)
Let 
be the number of
candidates in the Hiring Problem. Let 
be the probability
of hiring the best candidate under strategy k''.
(a) What's the optimum k to use (in the sense of maximizing
)? What's the value of this optimum (accurate to
three digits)?
(b) Give a rigorous proof that this is the optimum k to use.
(This part is harder.)