Personal Decision Making Problems

 

1 Missing dollar and accounting

Three men attending a convention at a hotel rent a booth for $30, and the manager found it costs only $25, and gave $5 to bellhop to give back to the three men.

The bellhop gave $1 to each man and pocketed the remaining 2 dollars.

Now, each man pay $9 plus the $2 to the bellhop give only $29. Where is the missing dollar?

 

2 Parking on the street illegally or in a lot?

Park in the lot, the rate is $10 if less than a hour or $14 more than a hour. 25% probability you will stay less than a hour.

Illegally on the street, 20% of time you will receive a tick of $30, 5% obstruction of traffic for $100, and 75% get off for free.

You decide.

 

3 DC Snipers and probability

Fall 2002 Washington, D.C. Police believe (which is true) that the sniper owns a whit van, a number of rifles, and a manual for snipers.

They did arrest a man owned all these items. How likely he is innocent?

Around 4 million people in suburban DC.

 

4 Monty Hall Problem and conditional probability

"21" trailer

http://www.youtube.com/watch?v=ZRzZX2aN3I0&feature=related

Monty Hall in "21"

http://www.youtube.com/watch?v=cXqDIFUB7YU&feature=related

Monty Hall explained

http://www.youtube.com/watch?v=mhlc7peGlGg&feature=related

 

5 Common knowledge and stock market

Married couples in a feminist village: each woman knows other woman's husband has been unfaithful but not when her own has.

Women are intelligent, not telling other women of their philandering husbands, and required to kill her husband the very day she can prove he has been unfaithful.

As it happens, there are twenty of the men have been unfaithful. Is there anyone going to be killed?

One day, a well trusted tribal matriarch from far side of the forest warns that there is at least one philandering husband among them. How about now?

 

6 American Genie and long term planning

 

7 St. Petersburg Paradox and utility

Flip a coin repeatedly until a tail first appears.

If flip once, win $2. Twice, win $4. Three times, $8. N times 2n dollars.

How much you willing to pay to play this game?

 

8 Prisoner's Dilemma and teamwork

A beautiful mind

http://www.youtube.com/watch?v=v5jrNoNNtrE

Prisonerís dilemma explained