Warm-Up 13, Due Thursday, April 22, before class.

Please answer each question in three or more sentences. It is OK to answer 'I don't know' - but try and state why you are confused! No late Warm Ups are accepted for any reason, and only those submitted electronically through this web page (or by email, if the web page has technical problems) are considered.

Your Name:

Question 1

Without doing the calculations, is the expected value for playing the lottery positive or negative, if you take the money for buying a lottery ticket? Give a sound reason.

Question 2

Three amounts of money, $10, $100, and $1000 are in three closed identical looking envelopes. After shuffling of these envelopes, one of them is given to you. What is the expected value?

Question 3

You saved the life of a very rich man. He wants to reward you with $1,000,000. "But wait a minute", he says. "We can also instead play a little game. We throw a fair coin, and if it shows head I give you $2,100,000, but if it shows tail I give you nothing. Do you want the $1,000,000 or do you accept the game?" What is the expected value of the game, and would you play the game or rather take the $1,000,000? Why?