Question

What is the probability that the sum of the numbers on two dice is at most 7

Answer 1

The probability of getting the sum of at most 7 is 0.583 or 21/36.

Explanation:

The sum from rolling two dice can be any value from 2 to 12.

As there are 6 numbers on one die and 6 on the other, the total number of ways the dice can fall is 36.

Let ( 1,4) represent rolling a 1 with the first die and a 4 with the second and so on.

A sum of 2 can be obtained in only 1 way -from (1,1)

A sum of 3 can be obtained in 2 ways - (1,2) and (2,1)

A sum of 4 can be obtained in 3 ways - (1,3) , (2,2) and (3,1)

A sum of 5 can be obtained in 4 ways - (1,4) , (2,3) , (3,2) and (4,1)

A sum of 6 can be obtained in 5 ways - (1,5) , (2,4) , (3,3) , (4,2) and (5,1)

A sum of 7 can be obtained in 6 ways - (1,6) , (2,5) , (3,4) , (4,3), (5,2) and (6,1)

A sum of 8 can be obtained in 5 ways - (2,6) , (3,5) , (4,4) , (5,3) , and (6,2)

A sum of 9 can be obtained in 4 ways - (3,6) , (4,5) , (5,4) and (6,3)

A sum of 10 can be obtained in 3 ways - (4,6) , (5,5) and (6,4)

A sum of 11 can be obtained in 2 ways - (5,6) and (6,5)

A sum of 12 can be obtained in 1 way - (6,6)

At most 7 means probability of getting the sum to be 7 or less.

So, sum of 2 + 3 + 4 + 5 + 6 + 7

Total possibilities = 1 + 2 + 3 + 4 + 5 + 6

                             = 21

The probability of getting the sum of at most 7 = 21/36

The probability of getting the sum of at most 7 = 0.583

Therefore, the probability of getting the sum of at most 7 is 0.583 or 21/36.