SOLUTION: When two dice are rolled find the probability of getting... a) a sum that is divisible by 3

Question 1203192: When two dice are rolled find the probability of getting...
a) a sum that is divisible by 3
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Answer: 1/3

Explanation:

A sum that is divisible by 3 means it is a multiple of 3
The multiples of 3 that are dice sums: 3, 6, 9, 12

There are a = 2 ways to roll a 3
1+2 = 3
2+1 = 3
There are b = 5 ways to roll a 6
1+5 = 6
2+4 = 6
3+3 = 6
4+2 = 6
5+1 = 6
There are c = 4 ways to roll a 9
3+6 = 9
4+5 = 9
5+4 = 9
6+3 = 9
And finally there is d = 1 way to roll a 12
6+6 = 12

That gives a total of a+b+c+d = 2+5+4+1 = 12 ways to get a multiple of 3
This is out of 6*6 = 36 possible dice rolls. Imagine a table that has 6 rows and 6 columns.

Therefore, 12/36 = 1/3 is the probability of getting a sum that is divisible by 3.

1/3 = 0.333 = 33.3% approximately

Other approaches can be found here
https://math.stackexchange.com/questions/506157/sum-of-two-dice-rolls-divisible-by-3

Answer by ikleyn(52810)   (Show Source): You can put this solution on YOUR website!
.

On rolling dice, see the lesson
    - Rolling a pair of fair dice
in this site.

Find there many typical solved problems of this type
with complete explanations and learn the subject from there.

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