When two balanced dice are rolled there are 36 possible outcomes. Find the probability that the sum is a multiple of 3 or greater than 4?

Answer 1

The above answer is wrong. It does not account for some possibilities like (4,5) and it duplicates (2,3) and (3,2) in the list that it gives. Accounting for all of this, changes the number of outcomes that satisfy the question to 32. So it is 32/36 not 28/36.

A note to students using a site for homework: Just because someone posts or gives you an answer, don't assume that it is correct. Question it and prove it to yourself. (even my answer) Use their answer(s) to help you understand the problem and approach. Don't just take their answer as being correct.

This is not an attack on the person who supplied this solution. Unintentional mistakes and typographical errors are possible in the real world. This is really a warning for those students that may be using sites like this. Don't just blindly accept answers provided. Don't just stop when you see an answer that someone says is correct. (or even if 1000's of people imply that it is correct) Seek to understand their approach and solution, and you will gain a greater benefit than just getting an answer. In the words of Yoda "A benefit greater than just an answer you will get, hmm? Yes, Yes."

Answer 2

Greater than 4 can be:

1, 4

1, 5

1, 6

2, 3

2, 4

2, 5

2, 6

3, 2

3, 4

3, 5

3, 6

and their opposites,

and

3, 3

4, 4

5, 5

6, 6

Total = 26 possibilities

Multiples of 3 that aren't already listed (not greater than 4): only '3'.

Ways to roll 3:

1, 2

2, 1

Total = 2 possibilities.

Total ways to roll a multiple of 3 or greater than 4 = 26 + 2 = 28 ways.

Probability = 28/36 = 7/9 = (77 and 7/9) percent