# When two balanced dice are rolled, there are 36 possible outcomes. What is the probability that the sum of the?

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When two balanced dice are rolled, there are 36 possible outcomes. What is the probability that the sum of the numbers on the dice is 6 or 9?

I came up with 5/12 am i wrong?

### 7 Answers

• Possible 6’s:

1+5

2+4

3+3

4+2

5+1

Possible 9’s:

3+6

4+5

5+4

6+3

9 possibilities out of 36. Or 1 out of 4. So yeah, you’re wrong.

• There is 1 way of rolling 2 or 12 2 ways each of rolling 3 or 11 3 ways of rolling 4 or 10 4 ways of rolling 5 or 9 5 ways of tolling 6 or 8 6 ways of rolling 7 36 ways in all. This has a pleasing symmetry to it. I always work out 2-dice problems from that table, rather than list the possible throws. Look up in the table 2 ways of throwing 11 and 5 ways if throwing 6 so total is 7 ways in 36 of rolling either 6 or 11. A similar table can be constructed for 3 dice. 1 way of rolling 3 or 18 3 ways each of rolling 4 or 17 6 ways of rolling 5 or 16 10 ways of rolling 6 or 15 15 ways of rolling 7 ir 14 21 ways of rolling 8 or 13 25 ways of rolling 9 or 12 27 ways of tolling 10 or 11 216 ways in all. Not so easy to remember But logical as 117 is not an option, to roll 9 and that is 3 less ways than the 28 you would expect and 118 is not available to roll 10, nor is 127 which is 9 ways less than the 36 you would expect = 27

• As others have said, just count the possible ways of doing it and divide by 36.

An important point to note is that 1,8 is NOT the same 8,1. You have to count them each separately. (although you only count 3,3 once, not twice). To make this clear, draw out a 6 by 6 grid, assign each column and row a number 1-6, then count the squares which add up to 9 or 6. You will see that 1,5 appears separately to 5,1, but 3,3 only appears once.

To make 6:

1,5

2,4

3,3

4,2

5,1

To make 9:

6,3

5,4

4,5

3,6

Five ways to make 6, four ways to make 9, so nine ways to make 9 or 6.

9/36=1/4

• Write down the possibilities and count them

1+5, 5+1, 2+4, 4+2, 3+3, 6+3, 3+6, 4+5, 5+4

• 1,1 1,2 1,3 1,4 1,5 1,6

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

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

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

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

6,1 6,2 6,3 6,4 6,5 6,6 are the possible outcomes

Hence the number of sum of 6 are 4 and that of 9 is also 4. Its 8/36 man!!! 😉

Source(s): Mathematician
• 1/5

2/4

3/3

for 6

9 would be

1/8

2/7

3/6

4/5

so it would be 7/32 I think I’m not sure

• Yes, you are wrong.

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