There are 216 permutations of three standard dice. Of these, there are exactly 10 that sum to 15, namely 3-3-6, 4-5-6, 4-6-5, 5-4-6, 5-5-5, 5-6-4, 6-3-6, 6-4-5, 6-5-4, and 6-6-3. The probability, then, of rolling a sum of 15 with three standard dice is 10 in 216, or 5 in 108, or about 0.04630.
Assuming:you are rolling two six-sided dice:"greater than 5" does not include 5Number of possible rolls = 36 (6x6)28 rolls satisfy "at least one die shows a 4 or the sum of the dice is greater than 5":(1, 4), (1, 5), (1, 6),(2, 4), (2, 5), (2, 6),(3, 3), (3, 4), (3, 5), (3, 6),(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),The probability that at least on die shows a 4 or that the sum of the dice is greater than 5 is 28/36, or 7/9, or approx. 77.8%
There are 36 permutations of two dice. Of those, 9 add up to a sum of 5 or 6... 1 + 4 = 5 2 + 3 = 5 3 + 2 = 5 4 + 1 = 5 1 + 5 = 6 2 + 4 = 6 3 + 3 = 6 4 + 2 = 6 5 + 1 = 6 The probability, then, of rolling a 5 or 6 with two dice is 9 in 36, or 1 in 4, or 0.25.
On two 6-sided fair dice:Rolling a sum of 5: 4 out of 36, or 11.11%Rolling a sum of 7: 6 out of 36, or 16.67%Rolling a sum of either 5 or 7: 10 out of 36, or 27.78%Here's why: Look at the dice as unique, (maybe one is red and one is blue). Then there are 36 different possible outcomes.The four that give a sum of 5: 1+4, 2+3, 3+2, 4+1.The six that give sum of 7: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1So there are 4 chances out of 36 (or 1 out of 9 = 11.11%) to get a sum of 5, and 6 chances out of 36 (or 1 out of 6 = 16.67%) to get a sum of 7. If you want either 5 or 7 as a sum, add the chances together to get 10 out of 36 (or 5 out of 18 = 27.78%)
There are 36 permutations of rolling two dice. Of these, 9 of them result in a sum of 9 or greater, specifically 6-3, 6-4, 6-5, 6-6, 5-4, 5-6, 4-5, 4-6, and 3-6. The probability, then, of rolling a sum greater than 8 on a pair of fair dice is 9 in 36, or 1 in 4, or 0.25.
There are 216 permutations of three standard dice. Of these, there are exactly 10 that sum to 15, namely 3-3-6, 4-5-6, 4-6-5, 5-4-6, 5-5-5, 5-6-4, 6-3-6, 6-4-5, 6-5-4, and 6-6-3. The probability, then, of rolling a sum of 15 with three standard dice is 10 in 216, or 5 in 108, or about 0.04630.
(1, 5, 6, 6), (2, 4, 6, 6), (2, 5, 5, 6), (3, 3, 6, 6), (3, 4, 5, 6), (3, 5, 5, 5), (4, 4, 4, 6), (4, 4, 5, 5).
Assuming:you are rolling two six-sided dice:"greater than 5" does not include 5Number of possible rolls = 36 (6x6)28 rolls satisfy "at least one die shows a 4 or the sum of the dice is greater than 5":(1, 4), (1, 5), (1, 6),(2, 4), (2, 5), (2, 6),(3, 3), (3, 4), (3, 5), (3, 6),(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),The probability that at least on die shows a 4 or that the sum of the dice is greater than 5 is 28/36, or 7/9, or approx. 77.8%
There are 36 permutations of two dice. Of those, 9 add up to a sum of 5 or 6... 1 + 4 = 5 2 + 3 = 5 3 + 2 = 5 4 + 1 = 5 1 + 5 = 6 2 + 4 = 6 3 + 3 = 6 4 + 2 = 6 5 + 1 = 6 The probability, then, of rolling a 5 or 6 with two dice is 9 in 36, or 1 in 4, or 0.25.
On two 6-sided fair dice:Rolling a sum of 5: 4 out of 36, or 11.11%Rolling a sum of 7: 6 out of 36, or 16.67%Rolling a sum of either 5 or 7: 10 out of 36, or 27.78%Here's why: Look at the dice as unique, (maybe one is red and one is blue). Then there are 36 different possible outcomes.The four that give a sum of 5: 1+4, 2+3, 3+2, 4+1.The six that give sum of 7: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1So there are 4 chances out of 36 (or 1 out of 9 = 11.11%) to get a sum of 5, and 6 chances out of 36 (or 1 out of 6 = 16.67%) to get a sum of 7. If you want either 5 or 7 as a sum, add the chances together to get 10 out of 36 (or 5 out of 18 = 27.78%)
1+2+3+4+5+6=211 + 2 + 3 + 4 + 5 + 6 = 21
The probability of rolling a sum of 8 with two dice is 5 in 36 or about 0.1389. 2 and 6 3 and 5 4 and 4 5 and 3 6 and 2
There are 36 permutations of rolling two dice. Of these, 9 of them result in a sum of 9 or greater, specifically 6-3, 6-4, 6-5, 6-6, 5-4, 5-6, 4-5, 4-6, and 3-6. The probability, then, of rolling a sum greater than 8 on a pair of fair dice is 9 in 36, or 1 in 4, or 0.25.
18
-7, 1 -6, 0 -5, -1 -4, -2 -3, -3
43
4 and 3(4 + 3 = 7)or 1 and 6(1 + 6 = 7)or 5 and 2(5 + 2 = 7)