# Two dice are rolled once. What is the probability of getting a multiple of 3 or a sum of 10? The answer, according to my book, is 5/12

Jun 2, 2017

5/12 is correct

#### Explanation:

The explanation is as follows,

You have 6 numbers in each dice, so the total number of combinations is 36 (6 X 6), we should think that it is less because the order of these numbers is not important to us, but in this problem it matters.

The multiples of 10 are (4,6) and (5,5). The first one can be obtained double the times as the second because it could be (4,6) or (6,4), while (5,5) can only be obtained as is.

Then we have that the combinations that are formed by different numbers have a value of 2 while the others have a value of 1.

Having in total 15 of 36 combinations when we combine the two conditions.

That fraction can be reduced by factorizing 3, obtaining at the end

$\frac{15}{36} = \frac{5}{12}$

Following are the 36 combinations possible for two dices, from there you can count tge ones that fulfill your conditions and see that they are 15.

11
12, 21
13, 31, 22
14, 41, 23, 32
15, 51, 24, 42, 33
16, 61, 25, 52, 34, 43
26, 62, 35, 53, 44
36, 63, 45, 54
46, 64, 55
56, 65
66