# Probability of getting a sum of 13

by karthik666
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 P: 11 Obtain the probability of getting a sum of 13, when four fair dice are rolled together once. if we do by just calculating all possible values of sum,then it will take more time. so,we can do above problem as Multinomial Coefficents of sum i.e.,x1+x2+x3+x4 = 13 where,1<= xi <= 6,for all 1<= i <= 4. i got stuck that form the above equation how can we obtain no.of.possible ways to get sum = 13. Thanks for Help.
 P: 418 Do you know how to calculate the probability of getting, for instance a 4 when two dice are rolled?
 P: 11 yes,it's easy,but here we have to find when four dices rolled together..
P: 418

## Probability of getting a sum of 13

Just extend the ideas then. How about a 9 with 3 dice?
 P: 11 your approach is correct upto 3 dice,but u cannot do for 4 dice
 P: 418 Why not?
 P: 11 it will take more than half-an hour,but in Exam it won't entertain such silly tasks!!
 Mentor P: 14,242 I just did it three different ways and it took less than a couple of minutes, total. What do you get using your half hour long approach?
 P: 11 may be u r saying Lie,probaility(saying a Lie)= 0.5.. ok,what is the answer that you got?
 Mentor P: 14,242 Aside: Stop using text speech. It's against our rules. Sentences start with a capital letter and end with one period. "u" is not a word. It's "you". The same goes for "r". Use "are". Regarding your "Lie", no, that is not the answer I obtained. You mentioned you know how to solve the probabilities with three dice rather than four. Imagine one of the four dice is red, the other three are white. The red die can come up as 1, 2, 3, 4, 5, or 6, each with probability 1/6. If it comes up 1, the white dice need to total to 12. What's the probability of rolling a sum of twelve with three dice? How do you combine that with the probability that the red die came up as a one? Now do the same for the red dice being a two (with the white dice now summing to 11), the red die being a three (with the white dice now summing to 10), and so on. This should not take half an hour to solve.
 Admin P: 22,346 Speaking of brute force: borek@raspberrypi ~/python $cat dices.py total = 0 i13 = 0 for d1 in range(1,7): for d2 in range(1,7): for d3 in range(1,7): for d4 in range(1,7): total += 1 if d1+d2+d3+d4 == 13: i13 += 1 print i13, total borek@raspberrypi ~/python$ python dices.py 140 1296