You are on a TV show

You are on a TV show

HomeWork 3.5

1.     You are on a TV show. You have been asked to either play a dice game ten times or accept a $100 bill. The dice game works like this: Top of Form
• If you roll a 1 or 2, you win
• If you roll a 3, you win
• If you roll a 4, 5, or 6, you lose 

Should you play the game? Use expected values and decision theory to justify your answer.
Yes, you should play because the expected value is positive.
Yes, you should play because the expected value is more than $100.    
No, you should not play because the expected value is negative.
No, you should not play because the expected value is less than $100.
 
2.     Consider the following scenario The twelve-number bet:
 (a)   Find the expected value of each $1 bet in roulette. (Round your answer to three decimal places.)
(b)  use the Law of Large Numbers to interpret it. (Round your answer to one decimal place.) Over time, you should expect to lose about _______________  cents for every dollar you bet

3.     Consider the following scenario The even-number bet:
(a)   Find the expected value of each $1 bet in roulette. (Round your answer to three decimal places.)
(b)  use the Law of Large Numbers to interpret it. (Round your answer to one decimal place.) Over time, you should expect to lose about _______________  cents for every dollar you bet

4.     Consider the following scenario The three-number bet:
(a) Find the expected value of each $1 bet in roulette. (Round your answer to three decimal places.)

(b) Use the Law of Large Numbers to interpret it. (Round your answer to one decimal place.) Over time, you should expect to lose about _______________  cents for every dollar you bet

5.     Consider the following scenario The five-number bet:
a) Find the expected value of each $1 bet in roulette. (Round your answer to three decimal places.)
(b) Use the Law of Large Numbers to interpret it. (Round your answer to one decimal place.) Over time, you should expect to lose about _______________  cents for every dollar you bet

6.     You are on a TV show. You have been asked to either play a dice game five times or accept a $50 bill. The dice game works like this:
 
• If you roll a 1, 2, or 3, you win.
• If you roll a 4 or 5, you lose
• If you roll a 6 you lose

Should you play the game? use expected values and decision theory to justify your answer.

Yes, you should play because the expected value is positive.
Yes, you should play because the expected value is more than $50.    
No, you should not play because the expected value is negative.
No, you should not play because the expected value is less than $50.

7.     Find the expected value of a $1 bet in six-spot keno if three winning spots pays $1 (but you pay $1 to play, so you actually break even), four winning spots pays (but you pay $1 to play, so you profit), five pays, and six pays
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