Determine if the events A
and B
are mutually exclusive, independent, or neither.
P(A)=0.3,P(B)=0.3,P(A and B)=0.07
a. Mutually Exclusive
b. Independent
c. Neither
c. Neither
Events A and B are not mutually exclusive because they have a non-zero intersection (P(A and B)=0.07), meaning they can both occur at the same time. They are also not independent because the probability of both events occurring together (P(A and B)=0.07) is not equal to the product of their individual probabilities (P(A)*P(B)=0.3*0.3=0.09). Therefore, the events A and B are neither mutually exclusive nor independent.