A standard pair of six-sided dice is rolled. What is the probability of rolling a sum greater than 8?

Question

My answer has to be a simplified fraction or a decimal rounded to four decimal places.

Answer 1

First, it is important to note that the results of the two dice are independent (that is, they do not affect each other). Thus, there are 6*6=36 possible outcomes.

Next, we must determine how many successes exist, because Probability=(number of successes)/(number of possibilities).

                       Second Die
         N    1   2   3   4   5   6 

         ---------------------------

F        1 |  2   3   4   5   6   7 

i   D    2 |  3   4   5   6   7   8

r   i     3 |  4   5   6   7   8   9

s  e     4 |  5   6   7   8   9  10

t         5 |  6   7   8   9  10 11

          6 |  7   8   9  10 11 12

P(sum>8) = 10 successes out of 36 possibilities
               = 10/36

               = 5/18

               = 0.2778

Answer 2

Possible totals are 2,3,4,5,6,7,8,9,10,11,12

 

4 numbers greater than 8 out of 11 possible numbers

 

P(>8) = 4/11