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# Help Needed – 2

11 replies to this topic

### #1 dark_magician_92

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Posted 18 January 2012 - 07:30 PM

My friend Found this somewhere and i calculated a different answer than what he told was. Plz mention ur approach and answer of this problem!!

Rules of Game:-

"We each get one die, the highest die wins. If we tie, I win, but since you always lose when you roll a one, if you roll a one you can roll again. If you get a one the second time you have to keep it."

What is each person's probability of winning?

What are the probabilities of winning if you can keep rolling until you get something besides a one?
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### #2 dark_magician_92

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Posted 18 January 2012 - 07:36 PM

Spoiler for answer as per him

Spoiler for what i calculated

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### #3 spamwolf

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Posted 18 January 2012 - 09:26 PM

Spoiler for the first case

I still haven't worked out the second question but suspect it's just a hair under 50%

*edit: corrected some typo's

Edited by spamwolf, 18 January 2012 - 09:30 PM.

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### #4 tonyd

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Posted 18 January 2012 - 09:46 PM

Spoiler for what I got

Edited by tonyd, 18 January 2012 - 09:56 PM.

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### #5 curr3nt

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Posted 18 January 2012 - 09:47 PM

Spoiler for ...

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### #6 curr3nt

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Posted 18 January 2012 - 10:03 PM

Spoiler for ...

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### #7 thoughtfulfellow

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Posted 19 January 2012 - 05:11 AM

Spoiler for ...

I concur the answer you have for #2.
Spoiler for Different explaination

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### #8 Common Zenz

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Posted 19 January 2012 - 05:31 AM

Your probability of winning given that I have a six is 1/6.
Your probability of winning given that I have a five is 2/6.
Your probability of winning given that I have a four is 3/6.
Your probability of winning given that I have a three is 4/6.
Your probability of winning given that I have a two is 5/6.
Your probability of winning given that I have a one is X.

Where X is one sixth the sum of the above without the final entry.

That is 15/36= 5/12

Your chances are one sixth the sum of the above with the calculated X (5/12).

That is 5/12 * (1 + 1/6) = 5/12 * 7/6 = 35/72

Well, I'll be darn. Never give a sucker an even break.
Spoiler for

Edited by Common Zenz, 19 January 2012 - 05:35 AM.

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### #9 dark_magician_92

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Posted 19 January 2012 - 03:41 PM

Thank you to all of you i.e.Common Zenz , Current, thoughtfulfellow, tonyd and spamwolf. All your answers are right. And now the funny thing, after checking your answers and method (which was quite different from mine), i decided to post my solution and it was while typing when i realized That I MADE ONE OF THE MOST SILLIEST MISTAKES bcoz of which the answer which shud have been = 37/72 = 111/216 , turned out to be 135/216. Similar sort of error was in the 2nd part. However i am glad that you all participated. Will post some problems, if i come across some and hopefully not mess up the answers
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### #10 Ozek

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Posted 19 January 2012 - 09:12 PM

For the first question, I used a 6x6 grid with the 36 possible outcomes, and came up with odds of 17 1/2 out of 36 that I would win if I was allowed to reroll one time if I got a dice roll of 1. This matches what others have calculated with math, at a 48.61% chance to win.

For the second part, you can't use a simple grid but what others posted looks good.
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