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Dice Probabilities Question

Started by ZWEIHÄNDER, January 23, 2013, 01:28:56 PM

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ZWEIHÄNDER

January 23, 2013, 01:28:56 PM
I've searched (and Googled) [and asked] over a dice probabilities question. Any help you can provide would be greatly appreciated!

1) What are the chances of generating 2 matching faces on 2d10?

2) What are the chances of generating 2 matching faces on 3d10?

3) What are the chances of generating 3 matching faces on 3d10?


Best,
Daniel
No thanks.

ggroy

#1
January 23, 2013, 01:40:04 PM
Quote from: ZWEIHÄNDER;6210241) What are the chances of generating 2 matching faces on 2d10?

10%


The other cases require more work to calculate.

ggroy

#2
January 23, 2013, 01:42:57 PM
Quote from: ZWEIHÄNDER;6210243) What are the chances of generating 3 matching faces on 3d10?

1%


For generating 4 matching faces on 4d10, the probability is 0.1%

For generating 5 matching faces on 5d10, the probability is 0.01%

etc ...

Emperor Norton

#3
January 23, 2013, 01:51:01 PM
Quote from: ZWEIHÄNDER;6210242) What are the chances of generating 2 matching faces on 3d10?

28% If I did my math correctly.

Assume first die rolled anything.

Second die has a 10% chance of matching the first die.

In the 90% chance that the second die didn't match the first die, the third die has a 20% chance of matching the first OR second die.

0.1=(0.9*0.2)=0.28

vytzka

#4
January 23, 2013, 01:55:10 PM
To find the probability for 2 matching numbers out of 3d10, we'll find the reverse probability - of rolling no matching faces (all different numbers).

The first die can be anything you want. The second die will have to be one out of 9 numbers not already rolled. The third die will have to be different from both of them, or one out of 8 remaining choices.

This gives us 10 * 9 * 8 = 720 combinations out of 1000, or 72%.

Subtract that from 100% and you'll get 28% to get doubles or triples.

If you want just the chance for doubles, subtract the 1% chance to roll the same numbers on all dice, so it's 27% for just doubles (not triples).



edit: dammit, Norton. Well, if we both got the same number, it has to be correct, at least.

ggroy

#5
January 23, 2013, 01:55:53 PM
Quote from: ZWEIHÄNDER;6210242) What are the chances of generating 2 matching faces on 3d10?

(From a rough mental calculation).

If it also includes the 3 matching faces cases:  30%

ggroy

#6
January 23, 2013, 02:08:49 PM
In my rough mental calculation, I counted all the possible configurations, but overcounted the 3 matching faces cases.

So subtracting out the overcounted cases, the probability is  (300-2*10)/1000 = 28%

Emperor Norton

#7
January 23, 2013, 02:11:12 PM
One of the reasons I love math is that we all came to the same answer through different ways /nerd.

arminius

#9
January 23, 2013, 03:12:20 PM
Quote from: ZWEIHÄNDER;621024I've searched (and Googled) [and asked] over a dice probabilities question. Any help you can provide would be greatly appreciated!

2) What are the chances of generating 2 matching faces on 3d10?
Exactly 2? Or at least 2?

I know this has been answered, but I'll use another method. For exactly 2, you want a result that looks like XXY, XYX, or YXX. We'll just take the chance of XXY and multiply it by 3. So the chance of getting X on the first die is of course 100%. The chance of matching that on the second die is 10%. The chance of NOT matching on the third die is 90%. Multiply across and you get 9%. So the chance of getting exactly 2 matching dice is 27%.

The chance of getting exactly 3 matching dice is 1%, so the chance of getting 2 or more matching dice is 27% + 1% = 28%.
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