Determine the probability of the following

Question

Two dice are rolled. Determine the probability of the following. ("Doubles" means both dice show the same number. Enter your probability as a fraction.)

rolling a number greater than 5 or doubles

The answer is not 1/6, 1/36, 7/36, 2/9

Answer 1

There are 36 total possible pairs of the dice:

1-1 2-1 3-1 4-1 5-1 6-1

1-2 2-2 3-2 4-2 5-2 6-2

1-3 2-3 3-3 4-3 5-3 6-3

1-4 2-4 3-4 4-4 5-4 6-4

1-5 2-5 3-5 4-5 5-5 6-5

1-6 2-6 3-6 4-6 5-6 6-6

Out of these, there are 6 possible doubles:

1-1, 2-2, 3-3, 4-4, 5-5, 6-6

Also, out of the original 36, there are 26 ways to get greater than 5:

5-1, 6-1, 4-2, 5-2, 6-2, 3-3, 4-3, 5-3, 6-3, 2-4, 3-4, 4-4, 5-4, 6-4, 1-5, 2-5, 3-5, 4-5, 5-5, 6-5,

1-6, 2-6, 3-6, 4-6, 5-6, 6-6

BUT, out of the second group (those totaling greater than 5), there are 4 we already counted as doubles:

3-3, 4-4, 5-5, and 6-6

So the total number of "successes" (either doubles or totaling greater than 5) are 6 + 26 - 4 = 28

So the probability of getting doubles or a total greater than 5 is 28/36 (which can be reduced to 7/9)