If you roll 2 dice and the you have a 1/9 chance of rolling a 5 and a 1/6 chance of rolling doubles then what is the chance of rolling either a 5 or doubles

Question

Find the probability of rolling a five or doubles on 2 six sided dice is the probability of rolling five is 1/9 and the chance of rollinh doubles is 1/6

Answer 1

The probability of the UNION of two events (one event or the other) is P(A) + P(B) - P(A and B).

 

In this case, P(A) (rolling a 5) = 1/9 and P(B) (rolling doubles) = 1/6.  But what is P(A and B)?

 

Well, if you think about it, there's no way to roll 5 AND doubles.  If you roll doubles, the sum of the two dice is going to be an even number, and 5 is odd.  You can't have the same on both dice and add up to 5!  So P(A and B) = 0.

 

So the answer is:  1/9 + 1/6 - 0 = 5/18.