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## Brain teaser: dice

Consider two perfectly weighted six sided dice.

What are the chances of rolling a 12?

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1 in 32

3. 1 in 21 and 1 in 7?

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Originally Posted by oldironmudder
1 in 32
you are correct sir!

5. Originally Posted by BTAutoMag
you are correct sir!
I know mine are wrong, but checking the sites I found, neither is this.

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the odds of me being wrong twice in one day is highly unlikly... but I am tired and math is rusty

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In order to roll a 12 you have to roll a 6 on each die

The odds of rolling a 6 on the first one is 1/6, the same on the second. This comes out to a 1/36 chance of rolling a 6 on both of them together.

With a seven it does not matter what is rolled on the first one. 1-6 will still allow you to get to seven with the roll of the other one. That means you are only concerned about one of them and the chance is 1/6 that it will hit the right number to add up to 7

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OMFG i wasnt wrong... I'm just blind

that was what I came up with I just saw the 32 and thought 36

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Actually a 7 can be by 6/1, 5/2, 4/3. So how does this change the odds? There are three combos, so does it increase or not affect the probability?

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Originally Posted by 1stTarget
Actually a 7 can be by 6/1, 5/2, 4/3. So how does this change the odds? There are three combos, so does it increase or not affect the probability?
A seven can be had regardless of what is rolled on the first dice.

The first one can be a 1, 2, 3, 4, 5, 6. This gives you 6/6 chances of rolling one of the two numbers you need. Then you just need the right number on the second one to get a total of seven which you have a 1/6 chance of rolling.

Out of the 36 possible combinations 6 of them result in seven - ie 6/36 or 1/6

6/6 on the first one multipled by 1/6 on the second one gives you 6/36

Rolling for a six the first one needs to be either a 1, 2, 3, 4, or 5. This gives you 5/6 possibilities. The second one then just has to match correctly meaning you have a 1/6. This gives you a 5/36 odds of rolling a 5.

I used this to demonstrate to my daughter odds the other night. It is between the simplistic coin flips (ie whats the chances of flipping two heads in a row) and between figuring odds in cards. Tonight we worked on figuring odds in cards and adjusting odds on the fly as more cards were in play and known.

Next week we aer going to discuss statistical sampling (ie if you flip a coin 50 times and get 49 heads there is a good chance the coin is not a naturally weighted coin). However in order to do that you need to understand probability first.

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