Question

Let A, B and C be three events. With set notation, denote the following events (a)...

Let A, B and C be three events. With set notation, denote the following events (a) - (e).

(a) A happens and neither B or C happens.

(b) Both A and B happen but C does not.

(c) At least one of A, B, C happens.

(d) None of A, B, C happens.

(e) Out of events A, B and C, at most one event happens.

(f) In words, what is event (A ∪ C) c ∪ B?.

(g) In words, what is event (A ∪ B ∪ C) c ?.

Math   Statistics-And-Probability   
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Answer #1

U means union, means intersection and Ac means complement of A.

(a) A happens and neither B or C happens - A (B U C)c

(b) Both A and B happen but C does not - A B Cc

(c) At least one of A, B, C happens- A U B U C

(d) None of A, B, C happens - (A U B U C)c

(e) Out of events A, B and C, at most one event happens (A B)c (A C)c (B C)c

(f) (A U C)c U B - A or C does not happen of B happens

(g) In words, what is event (A U B U C)c - A or B or C does not happen

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