A pair of dice is rolled and the sum of the numbers is noted. What is the probability that the sum of 8 does not occur?

Question

Could anyone help me with this problem? I can't seem to figure it out. 

Answer 1

Hi Hunter, if you roll a pair of dice, there is a total of 36 possible outcomes. If you set up a table, you can see what the outcomes are.

 

Example:

 

     1      2      3      4     5    6

-----------------------------------

1   2      3      4      5     6    7

 

2   3      4      5      6     7    8

 

...

 

6   7      8      9     10    11  12

 

 

There are 5 possible ways for the the sum to be 8, they are:

 

2 and 6, 3 and 5, 4 and 4, 5 and 3, and finally, 6 and 2.

 

Note, 2 and 6 is not the same as 6 and 2.

 

The probability of any number occurring is 1 in 36 or 1 / 36.

 

If the sum of 8 can be rolled in 5 ways, the probability of an 8 is: 1 / 36 + 1 / 36 + 1 / 36 + 1 / 36 + 1 / 36 or 5 / 36

 

Then the probability an 8 will not occur is: 1 - 5 / 36 or 31 / 36.

 

I could have added up all of the ways an 8 could not occur such as:

 

1 / 36 + 1 / 36 ... 1 / 36 = 31 / 36, but that is the hard way.

 

If I know the probability of something happening, I can then subtract it from 1 to find out the probability of it not happening.

 

Questions?