# SOLUTION: When two fair dice are rolled, the sum of the two dice can be any number from 2 through 12. What is the probability that this sum will be exactly a 7? Please show me how to solve

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 Question 72870: When two fair dice are rolled, the sum of the two dice can be any number from 2 through 12. What is the probability that this sum will be exactly a 7? Please show me how to solve this.Found 2 solutions by jmg, stanbon:Answer by jmg(22)   (Show Source): You can put this solution on YOUR website!This is hard to explain on here but I will try. If you look at all the possible combinations: 1+1=2 1+2=3 . . . 1+6=7 then go to the 2's, you have already used 1+ 2 so now start with 2+2=4 2+3=5 . 2+5=7 2+6=8 then go to the 3's, etc. When you finish with all the combos, up through 6+6. You will have a total of 21 combinations that could occur when rolling two fair dice. If you look through them you will see that there are 3 combinations that will add up to 7. So the probability that you will roll a sum of 7 is 3/21, which reduces to 1/7 Answer by stanbon(57411)   (Show Source): You can put this solution on YOUR website!When two dice are rolled there are 36 possible face patterns: 6*6 The patterns that give a sum of 7 are: (1,6)(2,5)(3,4)(4,3)(5,2)(6,1) So there are 7 of the 36 patterns that have a sum of 7. Therefore the probability of getting a sum of 7 is 7/36 Cheers, Stan H.