Math for life Homework, spring 2007
Class of Professor Georgi Stojanov
homework writer: Dennis Shasha

HOMEWORK: A has 20% of the supporters
B has 42%
C has 38%.

There are two one-against-one votes. 
A wins.
How is this possible? (Hint: think about where A should be in the political
spectrum.)

PROBABILITY
how to think of probability
lay out the list of equi-probable events.
7, 11 or doubles -- good bet or not
HOMEWORK: We found out in class that the above wins in 14 out of 36 cases.
You want to add a few other ways to win so that the better wins 18 out of
36 times.

PROBABILITY
Monty hall problem
analyze in class
HOMEWORK: 10 doors one has a treasure behind it. Others have sick goats.
Protocol: you choose a door.
Monty opens 7 other doors (all with goats).
You get to switch.
Quesitons: do you? If so, what is your likelihood of winning.




HOMEWORK: Suppose there were two people tied for tallest
call them T1 and T1'. T2 is the next in height.
Now there are 8 possible cases. What is your probability of getting
either T1 or T1'?
Use a protocol where you let the first half of the men go by
and then marry the next who is at least as tall as the tallest you've seen.


HOMEWORK: What if you could connect four towers in a day.
Then how long would it take to construct the towers?


COMPETITIVE OPTIMIZATION 
agent problem in a casino in Iguazu
If agent gets 20% of the money if someone loses and nothing
if someone wins, then agent and two players can guarantee to win.
For example, they play roulette.
Sabrina bets $950 on black, Josefine bets $950 on red,
and each bets $50 on green.
If the ball lands land on green, then they leave the casino with $3600.
If the ball lands on black, then Sabrina leaves with $1900 but the agent
Franziska gets $200 because of Josefine's loss.
Altogether the casino has paid out $2100 and received $2000.
Symmetrically if the ball lands on red.
HOMEWORK: can you arrange their bets so the three girls together will certainly
make $120 given a starting capital of $1000 each.