the probability for event a is 0.3, the probability for event b is 0.6, and the probability of events a or b…

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

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

Answer

Explanation:

Step1: Recall the formula for mutually - exclusive events

For mutually - exclusive events (A) and (B), (P(A\cup B)=P(A)+P(B)).

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

Given (P(A) = 0.3) and (P(B)=0.6), then (P(A)+P(B)=0.3 + 0.6=0.9).

Step3: Compare with (P(A\cup B))

Given (P(A\cup B)=0.8). Since (P(A)+P(B)=0.9\neq0.8 = P(A\cup B)), the events are not mutually - exclusive.

Answer:

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