What is the probability that you will roll doubles or a sum of two with two dice?

Question

You want to know the probability that you will roll doubles or a sum of two with two dice. What is the probability?

Answer 1

When we have a probability question that asks the probability of one event OR another event, we want to ADD the two probabilities together.

 

If the question were what is the probability of rolling a 3 or a 4 on one die, the answer would be the probability of rolling a 3 (1/6) PLUS the probability of rolling a 4 (1/6), or 2/6 = 1/3.

 

Here we have two dice. The number of different outcomes on two dice is the number of different outcomes on the first die (6) TIMES the number of different outcomes on the second (6), or 36.

 

The probability of rolling doubles is 1/6, because there are 6 ways to roll doubles. 6/36 = 36.

 

Now we want to count the number of ways of rolling a sum of two. There's only one: 1 and 1. 

 

However, 1 1 was already counted when we counted the number of ways to roll doubles. That is, there's no way to roll a sum of two without rolling doubles. So the number of ways of rolling doubles OR a sum of two is still only 6.

 

6/36 = 1/6.