Question

The probability for event A is 0.3, the probability for event B is 0.6, and the probability of events A or B is 0.8.

Why are the events not mutually exclusive?

The sum of P(A) and P(B) is less than P(A or B).
The product of P(A) and P(B) is less than P(A or B).
The product of P(A) and P(B) is not equal to P(A or B).
The sum of P(A) and P(B) is not equal to P(A or B).

mod note: Please do not give away the answer directly. Low-effort and/or plagiarized answers will be removed.

Answer 1

From the probability axioms, we know that if two events \(A\) and \(B\) are mutually exclusive, i.e., if \(A \cap B = \emptyset\), then we can write:
\(P(A \cup B) = P(A) + P(B).\)
Is this equality true for the given values of \(P(A \cup B) = 0.8\), \(P(A) = 0.3\) and \(P(B) = 0.6\)?