For a single roll of two dice, are rolling a sum of 6 and rolling doubles mutually exclusive events?

 They are not mutually exclusive events.

Step-by-step explanation:

Let A be the event of getting a sum of 6 on dice.

Let B be the events of getting doubles .

A={ (1,5), (2,4), (3,3), (4,2), (5,1) }

B = { (1,1) , (2,2), (3,3),  (4,4), (5,5), (6,6) }

Since we know that Mutaullty exclusive events are those when there is no common event between two events.

i.e. there is empty set of intersection.

But we can see that there is one element which is common i.e. (3,3).

So, n(A∩B) = 1 ≠ ∅

Hence, they are not mutually exclusive events.