Assignment 125Query

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course MTH 152

2/22 12

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

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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?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution: $3 for 6 =.50cents, $2 for 5=.33cents, and $1 for 4=.16cents

The fair price is $1

confidence rating #$&*: 3

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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 OK

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Self-critique Rating: OK

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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?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution: 18/36

confidence rating #$&*: 3

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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 Where did the 37 come from? Wouldn’t it be 18*2=36?

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Self-critique Rating: OK

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There are 37 slots, one of which isn't colored.

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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?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution: There isn’t a way to get a sum of 1 with two cards, there also isn’t a way to get a sum of 2 with two cards because the two lowest cards are 1 & 2 which = 3, there are two ways for 3 (1,2 & 2,1), there is two ways to for 4 (1,3 & 3,1) and four ways to get 5 (1,4 & 4,1 & 2,3 & 3,2)

confidence rating #$&*: 3

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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 Why did you include total ways for 7-9 if we were only looking at 2-5?

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Self-critique Rating: OK

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The cards themselves are numbered 1-5. We are drawing two cards.

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

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Self-critique (if necessary):

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Self-critique rating:

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

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Self-critique (if necessary):

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Self-critique rating:

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&#Good responses. See my notes and let me know if you have questions. &#