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

Question

What is the probablity that the sum will be less than 8? Please show me how you arrived at your answer.

Thank you everyone!

Answer 1

The following are the dice combinations which have sum less than 8:
1-1, 1-2, ..., 1-6, 2-1, 2-2,...,2-5, 3-1, 3-2, 3-3, 3-4, 4-1, 4-2, 4-3, 5-1, 5-2, 6-1
Note that I listed 1-2 and 2-1 separetely. Now there are 21 dice combinations above and there are a total of 36 combinations. So the answer is 21/36=7/12.

Answer 2

7/11

The answer by nikitty makes the most sense to me but she is a bit wrong. the smallest sum possible is 2 and the largest sum possible is 12. Absolutely every number between 2 and 12 (inclusively) is a sum of two numbers availabel on the dice. therefore there are 11 possible outcomes each of which have the exact same probablity of coming true. 7 of these outcomes happen to be less than 8. So the probability of landing a number <8 is 7/11

Answer 3

Total outcomes = 36 (6 x 6)
Outcomes with sum less than 8 = 21

Probability = 21/36 = 7/12

Answer 4

Take the combinations that add upto less than 8 for two dice (Dice 1 and Dice 2 in that order)
{1,6}, {6,1}, {2,5}, {5,2}, {3,4}, {4,3} - adds to total 7 < 8
{1,5}, {5,1}, {2,4}, {4,2}, {3,3} - adds to total of 6 < 8
{1,4}, {4,1}, {2,3}, {3,2} - adds to total of 5 < 8
(1,3}, {3,1}, {2,2} - adds to total of 4 < 8
you see this are reducing by one less for each total less than before
Sure enough -
(1,2}, {2,1} - adds to total of 3 < 8
{1,1} - adds to total of 1 < 8
Total no. of combinations (count above combinations) adding to less than 8 - 6+5+4+3+2+1 = 21
Totl possible different combinations of the two dice (any of the 6 for Dice 1) * (any of the 6 for dice 2)
= 6 * 6 = 36 total possible combinations for the dice
So probability of sum less than 8 - 21/36 = (7*3)/(12*3) = 7/12 - =0.5833

Answer 5

1 dice 3! =1x2x3 = 6 and 2 dice 4!= 1x2x3x4= 24 and 6! 1x2x3x4x5x6=720 ; 720 x 6 x 24 = C

Answer 6

Write down each possible outcome, there are 6*6 possible outcomes. Count the ones that are less than 8. Divide by 36. That's the probability

Answer 7

for 7 there are 6 ways
for 6 thereare 5ways
for 5 there are 4 ways
for 4 thereare 3 ways
for 3 there are 2 ways
and for 2 there is 1 way
so fav events=21
sample space=36
p=21/36=7/12

Answer 8

7 out of 12 twelve chance
58.333 percent

36 possibilites and 15 of them add to 8 or higher.

36-15 = 21
21/36

Answer 9

the probabilty is 7 of 12 times

Answer 10

the highest sum is 6+6=12
the lowest is 1+1=2
so we have 10 posibilities to work with
8/10=80%