**Answer:**

a) not independent

b) not mutually exclusive

**Step-by-step explanation:**

**Given:**

- A 6 sided die is rolled

- Event A is rolling an even number

- Event B is rolling a prime number

**Find**

- (a) Are A and B independent events?

- (b) Are A and B mutually exclusive events?

**Solution:**

- We will find the probability of each event:

set(Even number: A) = {2, 4, 6} = 3 outcomes

set(Prime number: B) = {2 , 3, 5} = 3 outcomes

- The probabilities are:

P(A) = 3/6 = 0.5

P(B) = 3/6 = 0.5

- For Event A and B to be independent then the following condition must match:

P ( A & B ) = P(A)*P(B)

set (A&B) = {2} = 1 outcome

P(A&B) = 1/6

1 / 6 = 0.5*0.5

1/6 = 0.25 ...... NOT INDEPENDENT

- For Event A and B to be mutually exclusive then the following condition must match:

P(A&B) = 0

P(A&B) = 1/6

Hence, we can say the events are NOT MUTUALLY EXCLUSIVE