Assigned Wednesday, 4/10:
Read Sections 6.6
Complete the following problems:
6.6: 11, 16, 19, 24, 26, 28
MiniProject 2: The Monty Hall Problem (due Wednesday, 4/17)
Below are three exercises based on the Monty Hall Problem.
1. Suppose that you are given three doors to choose from as in the Monty
Hall Problem. Now, however, Monty will choose a door AT RANDOM and show
you what's behind it. If he chooses the door that you chose, and it has
the car, you win (the game is over). If he chooses the door that you've
chosen and it has a goat, you lose (the game, again, is over). If he
chooses a door that you didn't choose and it has the car, you lose
automatically. If he chooses a door that you didn't choose and it has a
goat, then he presents you with the option of switching or staying.
Should you switch? What is your overall probability of winning this
game. (Hint: Use a tree diagram)
2. Suppose that Monty Hall presents you with four doors instead of 3
(three goats and one car). After you select a door, he'll open one of
the unopened doors and show you a goat, then allow you to switch if you
want. He'll then open one of the remaining unopened doors and show you
another goat, and then allow you the choice of the two remaining doors.
Determine the optimal strategy by calculating the probabilities
associated with each. Again, a tree diagram may be helpful.
3. Suppose that Monty Hall presents you with four doors, but now there
are two cars and two goats. You choose a door, then he opens one of the
unchosen doors and shows you a goat. He gives you the option of
switching doors. Should you? Find the probability that you win in each
case.
Complete thse three exercises. In addition, write a letter intended for
Parade Magazine columnist Marilyn vos Savant, defending her position on
the original problem that your probability of winning increases to 2/3
when you switch. The letter should include an explanation of the problem
and should try to overcome the average reader's intuition that the chances
are 50-50.
COURSE INFO