5,6,2,3,9 has a greater sum than 10,4,5,1 and 2 which has a sum of 22.
When 2 dice are rolled, the probability of getting a sum less than 4 or greater than 9 is 2 in 9. There are 36 permutations of two six sided dice, 1-1, 1-2, ..., 1-6, 2-1, ... 2-6, ..., 6-1, 6-2, ... 6-6. Of these permutations, 3 have a sum less than four, 1-1, 1-2, and 2-1, and 5 have a sum greater than nine, 4-6, 5-5, 5-6, 6-4, 6-5, and 6-6. Add these probabilities together and you get (3 + 5) in 36, or 8 in 36, or 2 in 9.
43
A sum of 9 with 2 dice can be achieved with 3+6, 4+5, 5+4, and 6+3, so there are 4 elements in the event space for a sum of 9. This corresponds to a probability of 4 in 36, or 1 in 9, or about 0.1111 for that result.
Sum = 42 Count = 6 Mean = Sum/Count = 42/6 = 7
There is no sequence of adds or subtracts of 5, 6, 8, 9, and 10 that sum to 1. Check it with this C++ code... for (int i=0; i<32; ++i) { int sum = 0; if (i&1) sum += 5; else sum -= 5; if (i&2) sum += 6; else sum -= 6; if (i&4) sum += 8; else sum -= 8; if (i&8) sum += 9; else sum -= 9; if (i&16) sum += 10; else sum -= 10; cout << i << " " << sum << endl; }
6+5=11 2 ess gives you 9
5,6,2,3,9 has a greater sum than 10,4,5,1 and 2 which has a sum of 22.
When 2 dice are rolled, the probability of getting a sum less than 4 or greater than 9 is 2 in 9. There are 36 permutations of two six sided dice, 1-1, 1-2, ..., 1-6, 2-1, ... 2-6, ..., 6-1, 6-2, ... 6-6. Of these permutations, 3 have a sum less than four, 1-1, 1-2, and 2-1, and 5 have a sum greater than nine, 4-6, 5-5, 5-6, 6-4, 6-5, and 6-6. Add these probabilities together and you get (3 + 5) in 36, or 8 in 36, or 2 in 9.
43
There are 36 permutations of two dice. Of them, 6 have a sum of 7, (1+6, 2+5, 3+4, 4+3, 5+2, and 6+1) and 2 have a sum of 11 (5+6 and 6+5). The probability, then of getting a sum of 7 or 11 is (6 plus 2) in 36, or 8 in 36, or 2 in 9, or about 0.2222.
The sum of 6/18 and 2/9 is 5/9.
4/6, 5/5, 5/6, 6/4, 6/5, 6/6 ie 6 out of 36.
A sum of 9 with 2 dice can be achieved with 3+6, 4+5, 5+4, and 6+3, so there are 4 elements in the event space for a sum of 9. This corresponds to a probability of 4 in 36, or 1 in 9, or about 0.1111 for that result.
6(5 + 9) = (6 x 5) + (6 x 9) = 6 x 14 = 84
Sum = 42 Count = 6 Mean = Sum/Count = 42/6 = 7
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.