Either/Or Probabilities

Question

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

Compute the probability.

(Round to three decimal places.)

Answer 1

As I stated before, there are 36 different combinations that can be rolled.

 

There are 6 ways to roll doubles:  1/1, 2/2, 3/3, 4/4, 5/5, 6/6.  So the probability of rolling doubles is 6/36 = 1/6

 

There are 3 ways to roll 10:  4/6, 5/5, 6/4.  So the probability of rolling 10 is 3/36 = 1/12.

 

So the probability of rolling double OR 10 is P(doubles) + P(ten) - P(doubles AND 10).

 

There's only one way to roll doubles and 10, and that's 5/5.  So the probability of that is 1/36

 

So the answer is 1/6 + 1/12 - 1/36 = 8/36 = 2/9 = 0.222