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

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joaobezerra joaobezerra · Answer 1 · 2020-02-05T23:36:53+01:00

Answer:

c) Either A or B or both occur.

Step-by-step explanation:

Suppose that we have two events

Event A

Event B

We have that:

[tex]A = a + (A \cap B)[/tex]

In which a a happens and b does not and [tex]A \cap B[/tex] is the probability that aboth events happen

By the same logic, we have that:

[tex]B = b + (A \cap B)[/tex]

The union of events A and B is:

[tex](A \cup B) = a + b + (A \cap B)[/tex]

Which includes either one of them or both.

So the correct answer is:

c) Either A or B or both occur.