During a given month, p(a)=0.75,p(b)=0.6, and p(a and b)=0.5. are these two events independent? are they mutually exclusive? a. yes; yes b. yes; no. no; yes c. no; no. d. it cannot be determined

Two events are mutually exclusive when the probability that both events happen equals the product of the probability that both events happen individually.
i.e. P(A and B) = P(A) x P(B)
Here, P(A and B) = 0.5 but P(A) x P(B) = 0.75 x 0.6 = 0.45
Therefore, the two events are not independent.

Two events are said to be mutually exclusive when P(A and B) = 0. Here P(A and B) ≠ 0.
Therefore, the two events are not mutually exclusive.

Therefore, option C is the correct answer.

What are the options