Suppose that events a and b are mutually exclusive with p (a) = ½ and p (b) = ⅓.

a. are a and b independent events? explain how you know.

No, a & b are not independent if they're mutually exclusive.

Mutually exclusive means the two events cannot occur simultaneously. So if "a" happens "b" cannot. In contrast, two events are independent if the occurrence of one has no effect on the occurrence of the other.