Please help me with this probability problem. 2 dice are rolled and their sum is recorded.?

Question

What is the probability of the sum being less than 8? Please show me how you arrived at your answer.

Thank you everyone!

Answer 1

There are 36 possible outcomes form rolling two dice.
2: 1-1
3: 1-2, 2-1
4: 1-3, 2-2, 3-1
5: 1-4, 2-3, 3-2, 4-1
6: 1-5, 2-4, 3-3, 4-2, 5-1
7: 1-6, 2-5, 3-4, 4-3, 5-2, 6-1
8: 2-6, 3-5, 4-4, 5-3, 6-2
9: 3-6, 4-5, 5-4, 6-3
10: 4-6, 5-5, 6-4
11: 5-6, 6-5
12: 6-6

21 out of 36 possible rolls result in 7 or less.
Therefore, there is a 21/36 chance of rolling less than 8.
(That comes out to about a 58.33% chance.)

(And YES, there is a difference between 3-4 and 4-3, for example. The order matters because each dice is unique. If it helps, try to imagine that you have a red die and a green die.)

Answer 2

Sides on each die = 6
Hence probability of two dice will be 6 * 6 = 36

For the sum to be less than 8 :
1) 6+1
2) 5+2
3) 5+1
4) 4+3
5) 4+2
6) 4+1
7) 3+4
8) 3+3
9) 3+2
10) 3+1
11) 2+5
12) 2+4
13) 2+3
14) 2+2
15) 2+1
16) 1+6
17) 1+5
18) 1+4
19) 1+3
20) 1+2
21) 1+1

Hence the probability of the sum of the two dice being less than 8 is 21 out of 36 or that is 58.33%

Answer 3

21/36

There are 36 combinations of two dice.
Here's how it breaks down--

There is 1 way to roll 2
2 ways for 3
3 ways for 4
4 ways for 5
5 ways for 6
6 ways for 7
5 ways for 8
4 ways for 9
3 ways for 10
2 ways for 11
1 way for 12

If you count up these probabilities you see there are 36 different combinations.
Count how many combinations are 7 or under and you arrive at 21. So 21 out of the total of 36 are under 8.
The probability is 21/36.

Answer 4

There is a 100% chance of them being less than 8.

Proof?

My bank balance.

It's now empty!

Answer 5

Damn, beaten! PJ is completely right.