If your solution to stated problem does not match the given solution, you should self-critique per instructions at

http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.

Your solution, attempt at solution. 

If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it.  This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

010.   Query 10

question: Query   12.5.6  fair dice game pays $3 for 6, $2 for 5, $1 for 4.  What is a fair price to pay for playing this game?

Your solution: 

Confidence Assessment:

Given Solution: 

`aA 1 in 6 chance of getting $3 is worth 1/6 * $3 = $.50 .

A 1 in 6 chance of getting $2 is worth 1/6 * $2 = $.33 1/3 .

A 1 in 6 chance of getting $1 is worth 1/6 * $1 = $.16 2/3 .

The total expectation is  $1.00 * 1/6 + $2.00 * 1/6 + $3.00 * 1/6 = $1.00

So a fair price to pay is $1.00 **

 Self-critique

question: Query   12.5.10  expectation Roulette $1 bet 18 red, 18 black one zero

What is the expected net value of a bet on red?

Your solution: 

Confidence Assessment:

Given Solution: 

`aIf your net gain is $1 for a win and -$1 for a loss the expected value is

18/37 * (+1) + 19/37 * (-1) = -$.027. **

 Self-critique

question: Query   12.5.20  exp sum of 2 of 5 cards 1-5. 

What is the expected sum of the numbers on the two cards drawn?

Your solution: 

Confidence Assessment:

Given Solution: 

`aYou can't get a sum of 1 on two cards.  There is also no way to get a sum of two, since the lowest total possible is 1 + 2 = 3.

There are 2 ways to get total 3.  You can get 1 on the first and 2 on the second, or vice versa.

There are 2 ways to get total 4.  You can get 1 on the first and 3 on the second, or vice versa.

There are 4 ways to get total 5.  You can get 1 on the first and 4 on the second, or vice versa, or 2 on the first and 3 on the second, or vice versa.

There are 4 ways to get total 6.  You can get 1 on the first and 5 on the second, or vice versa, or 2 on the first and 4 on the second, or vice versa.

There are 4 ways to get total 7.  You can get 2 on the first and 5 on the second, or vice versa, or 4 on the first and 3 on the second, or vice versa.

There are 2 ways to get total 8.  You can get 3 on the first and 5 on the second, or vice versa.

There are 2 ways to get total 9.  You can get 4 on the first and 5 on the second, or vice versa.

You can't get more than 9.

There are 2+2+4+4+4+2+2 = 20 possibilities, so the probabilities are 2/20, 4/20, 5/20, etc..

The expected sum is therefore

2/20 * 3 + 2/20 * 4 + 4/20 * 5 + 4/20 * 6 + 4/20 * 7 + 2/20 * 8 + 2/20 * 9.

This gives 120 / 20 = 6. **

 Self-critique

question: Query   Add comments on any surprises or insights you experienced as a result of this assignment.