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).

Explanation:

Step1: Recall mutual exclusivity rule

For mutually exclusive events, $P(A \text{ or } B) = P(A) + P(B)$

Step2: Calculate sum of P(A) and P(B)

$P(A) + P(B) = 0.3 + 0.6 = 0.9$

Step3: Compare to P(A or B)

Given $P(A \text{ or } B) = 0.8$, $0.9
eq 0.8$

Answer:

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