What is the probability the sum of dice is not 3?

Answer 1

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 %