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? \bigcirc the sum of p(a) and p(b) is less than p(a or b). \bigcirc the product of p(a) and p(b) is less than p(a or b). \bigcirc the product of p(a) and p(b) is not equal to p(a or b). \bigcirc the sum of p(a) and p(b) is not equal to p(a or b).

Explanation:

Step1: Recall Mutually Exclusive Rule

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

Step2: Calculate \( P(A) + P(B) \)

Given \( P(A) = 0.3 \), \( P(B) = 0.6 \), so \( P(A) + P(B) = 0.3 + 0.6 = 0.9 \).

Step3: Compare with \( P(A \text{ or } B) \)

Given \( P(A \text{ or } B) = 0.8 \). Since \( 0.9
eq 0.8 \), the sum of \( P(A) \) and \( P(B) \) is not equal to \( P(A \text{ or } B) \), so events are not mutually exclusive.

Answer:

D. The sum of \( P(A) \) and \( P(B) \) is not equal to \( P(A \text{ or } B) \)