You are rolling two dice at the same time. What is the probability of rolling a sum of 5 or 9?

1 Answer
May 23, 2018

#5: 1/9#
#9: 1/9#

Explanation:

First, we can take a look at all of the #36# possible outcomes of rolling two dice. Remember, the two results are independent.

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Possibility of 5
We can check the table to see which results sum to #5#.

#(4,1)#
#(1,4)#
#(3,2)#
#(2,3)#

We could do this even without the table because of an understanding of the numbers that sum to #5#.

There are #4# possibilities that sum to #5# out of the total #36# possibilities. The probability is #4/36# or #1/9#.

Possibility of 9

We can apply the same principles as before to this problem.

Checking the table, we see that the following sum to #9#.

#(6,3)#
#(3,6)#
#(5,4)#
#(4,5)#

There are other combination that sum to #9#, such as #(7,2)#, but they exceed the limits of the dice.

Therefore, we again have #4# possibilities and a #1/9# probability.