The Answer Is:
34/36 = 17/18 = .94444 or 94.444 %
To get this Answer, You Do The Following:
Find what the probability is that the SUM of 2 Dice IS 3.
This means:
Die 1 equals 1 & Die 2 equals 2
or
Die 1 equals 2 & Die 2 equals 1
So ONLY 2 Variations of the Dice ALLOWS for them to SUM UP TO 3
Now Determine the TOTAL number of VARATIONS (SUMMING UP TO ANYTHING):
Since a Die Has 6 Sides and We need to Calculate the Variations of 2 DICE with 6 SIDES, We can Find the TOTAL NUMBER OF VARIATIONS by Doing this:
TOTAL VARIATIONS FOR 2 DICE = (NUMBER OF SIDES)(NUMBER OF DICE)
36 = 62
Then since we know ONLY 2 Variations OUT OF ALL VARIATIONS ALLOW THE DICE TO SUM UP TO 3 we know THE PROBABILITY of the Dice Summing up to 3 is:
(Number of Variations That SUM up to 3) / (TOTAL NUMBER of Variations)
2 / 36 = 1 / 18 = .05556 or 5.556 %
And Since We need to Determine the Probability of the Sum NOT being 3 WE need to Subtract the Probability of the DICE Summing up to 3 FROM 100% (or 36/36 = 1.00 = 100%)
So To Get The ANSWER We Just Do a SIMPLE subtraction:
SINCE: 100% = 1.00 = 1/1 = 36/36
So We Do The Subtraction To Find WHAT PROBABILITY The SUM IS NOT 3:
36/36 - 2/36 = 34/36 = 17/18 = .94444 or 94.444 %
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The probability is 25/216 = 0.1157, approx.
The probability of not rolling a sum of six with two fair dice is 1 minus the probability of rolling a sum of six. There are 36 permutations of rolling two dice. Of these, five sum to six, 1+5, 2+4, 3+3, 4+2, and 5+1. The probability, then of rolling a sum of six is 5 in 36. The probability, then of not rolling a sum of six is 31 in 36, or about 0.8611.
It is 17/18.
The probability is 27/216 = 3/8 = 0.125
It is 2/36 = 1/18