anaid23
Joined: Jul 21, 2012
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July 21st, 2012 at 11:42:22 AM permalink
A die is rolled, find the probability that an even number is obtained?
UP84
Joined: May 22, 2012
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July 21st, 2012 at 11:53:15 AM permalink
On the Blue die do you mean 1 1 1 7 7 7? You only have two 7s.
Also on the Green die, do you mean 2 6 2 6 2 6? You only have two 6s
"My aim, then, was to whip the rebels, to humble their pride, to follow them to their inmost recesses, and make them fear and dread us. Fear is the beginning of wisdom." ----- William Tecumseh Sherman
odiousgambit
Joined: Nov 9, 2009
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July 21st, 2012 at 11:58:34 AM permalink
this one looks really simple, you don't have to work out all the possibilities seems to me.
but I think you should do your own homework.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
7craps
Joined: Jan 23, 2010
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July 21st, 2012 at 11:59:45 AM permalink
Great question.
I know the answer but will keep it to myself for now.

Here is a pdf link to help answer these type of questions.
http://www.madandmoonly.com/doctormatt/mathematics/dice1.pdf
From: Matthew Conroy's page of mathematics
http://www.madandmoonly.com/doctormatt/mathematics/mathematics.htm

Looks to be similar to question #25
current version July 1, 2012
winsome johnny (not Win some johnny)
Triplell
Joined: Aug 13, 2010
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July 21st, 2012 at 11:59:59 AM permalink
Quote: anaid23

Blue dice has 1 1 1 1 7 7
yellow dice has 4 4 4 4 4 4
green dice has 2 6 2 6 2 2
orange dice has 3 5 3 5 3 5

Four dice with varying numbers on each face. You and three friends will play a simple game where you will each roll one of the dice and the highest number wins. You get first pick from the dice.

Question: Which die should you choose in order to maximize your chance of winning?

I believe the yellow and orange dice have same odds of winning/being the best choice of dice.
anaid23
Joined: Jul 21, 2012
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July 21st, 2012 at 12:00:13 PM permalink
blue has two 7s and four 1s

green has four 2s and two 6s
shakhtar
Joined: Nov 24, 2011
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July 21st, 2012 at 2:13:33 PM permalink
This seems incredibly simple, so perhaps I'm missing something because it seems obvious.

4 die, all 6 sided are rolled. This means there are 1296 combinations that can be rolled. Obviously Blue dice win 432 times, since two of their sides are higher than every other die roll (2x6x6x6). The other colors all win 288 times each, therefore, the answer is :

BLUE

Odds on who wins :

blue 2-1
yellow 7-2
green 7-2
orange 7-2

If we put a 5% vig on the prop, we would offer : blue +185, yellow +327, green +327, orange +327
tupp
Joined: Feb 9, 2012
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July 21st, 2012 at 2:48:42 PM permalink
Quote: shakhtar

Odds on who wins :
blue 2-1
yellow 7-2
green 7-2
orange 7-2

Isn't 7:2 a higher probability than 2:1?
shakhtar
Joined: Nov 24, 2011
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July 21st, 2012 at 3:57:46 PM permalink
Quote: tupp

Isn't 7:2 a higher probability than 2:1?

no. 2-1 equals a 33.33% chance of occurring, 7-2 equals a 22.22% chance of occurring

odds are a reflection of the chances of something occurring vs. the chances of something not occurring.

I'm assuming you don't do too much gambling, and by the oft chance that you do, you should probably find another hobby.
tupp
Joined: Feb 9, 2012
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July 21st, 2012 at 4:26:20 PM permalink
Quote: shakhtar

no. 2-1 equals a 33.33% chance of occurring, 7-2 equals a 22.22% chance of occurring

odds are a reflection of the chances of something occurring vs. the chances of something not occurring.

I'm assuming you don't do too much gambling, and by the oft chance that you do, you should probably find another hobby.

No need for the the personal comments.

I do not wish to seem pedantic nor start a semantics argument. However, for the ratios to match "the chances of something occurring vs. the chances of something not occurring," would not the ratios actually have to be inverted, to 1:2 and 2:7, respectively?

Furthermore, even if we invert the ratios, they do not match the percentages given. 1/2≠33.33%, and, likewise, 2/7≠22.22%.

On the other hand the percentages do match another ratio: the chances of something occurring vs. the total possibilities. So, 1/(1+2)=33.33%, and 2/(2+7)=22.22%.

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