Question 470584: What is the probability of getting an 11 when you roll two fair six-sided dice?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! There are 36 possible combinations when you roll a pair of dice. Starting with rolling a two ( one possibility - a one showing on each of the two dice). Then rolling a three (two possibilities - either a one on the first die and a two on the second die, or a two on the first die and a one on the second). You can continue through all the possibilities until you roll a 12 (one possibility - a six on each of the two dice). As stated earlier, if you add up all the possible combinations you will find that there are 36 of them.
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As to rolling an 11 -- there are two possible ways -- getting a six on the first die and a five on the second, or getting a five on the first die and a six on the second. So out of 36 possible outcomes, there are two chances that you can get the desired outcome of 11.
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This means that the probability that on a given roll you have a 2 in 36 chance of getting an 11. (This ratio of 2 to 36 can be reduced to an equivalent 1 in 18 chance ... meaning that if you roll a pair of fair dice 18 times you have about one chance of getting an 11.
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This probability can also be expressed as a percent by dividing 2 by 36 or 1 by 18 and converting the result to percent. If you do that division you will find that on a given roll of two fair dice you have a 5.5555555% chance of getting an 11.
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Hope this helps you understand probability of outcomes on pairs of dice. Just for info, there are 6 ways to roll a 7, (1-6,6-1, 2-5, 5-2, 3-4, 4-3) and that makes it the most likely outcome when you roll a fair pair of dice. The probability of getting a 7 on a given roll is 6 in 36 or 1 in 6 or 16.6666666%.
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