Question

The union of two events A and B is the event that: a) The intersection of A and B does not occur. b) Both A and B occur. c) Either A or B or both occur. d) Either A or B, but not both occur. e) A and B occur at the same time. f) None of the above

Answer 1

c) Either A or B or both occur.

Explanation:

Suppose that we have two events

Event A

Event B

We have that:

`A = a + (A \cap B)`

In which a a happens and b does not and
`A \cap B` is the probability that aboth events happen

By the same logic, we have that:

`B = b + (A \cap B)`

The union of events A and B is:

`(A \cup B) = a + b + (A \cap B)`

Which includes either one of them or both.

So the correct answer is:

c) Either A or B or both occur.