Two dice are rolled. E is the event that the sum is even, F is the event of rolling at least one six, and G is the event that the sum is eight. List the outcomes for the following events: a. E ∩ F {(2, 2), (4, 4), (6, 6)} {(6, 2), (6, 4), (6, 6), (2, 6), (4, 6)} {(2, 6), (4, 6), (6, 6)} ∅
b. Ec ∩ G {(6, 2), (6, 4), (6, 6), (2, 6), (4, 6)} {(2, 6), (4, 6), (6, 6)} {(2, 2), (4, 4), (6, 6)} ∅

(a)

(b)

Step-by-step explanation:

The sample space of two dice rolled is given below:

For Event E (The sum is even), the outcomes are:

For Event F (Rolling at least one six), the outcomes are:

For Event G (The sum is eight), the outcomes are:

(a)

Therefore:

(b)

E is the event that the sum is even

Therefore:

Since G is the event that the sum is eight( which is even), the intersection of the complement of E and G will be empty.

Therefore: