Suppose your sample space is the set of all US residents. Your experiement consists of choosing one US resident at random.

(a) Give an example of two events A and B that are independent.

(b) Give an example of two events A and B that are mutually exclusive.

(c) Give an example of two events A and B that are neither independent nor mutually exclusive.

Hint for 5: Recall that mutually exclusive events cannot occur at the same time. For example, living in California and living in Nevada are mutually exclusive (you cannot live in two states at a time). Recall that events are independent when knowledge that one event has occured affects the probability that the other event has occured. For example, being a basketball player and being over 6ft tall are not independent since basketball players are more likley to be over 6ft than the average person is.