Answer:
Step-by-step explanation:
a) Two events A,B are said to be mutually exlusive if any of the following occurs.
- A and B have an empty intersection
- A= B^c and their union is the whole sample space
- P(A intersection B) =0
REcall the following formula
Note that P(A) + P(B) = 1.1. Since the probability is always a number between 0 and 1, it must happen that , otherwise,
would have a probability greater than 1. Hence, A, B are not mutually exclusive.
b) by definition, if two events are indepent, we have that the probability of the intersection is equal to products of their probabilites. Or
c) Recall that if we have mutuallly exclusive events A, B, then we have that , if they were independent, we would have the following
which necesarilly implies that at least one of the two events has 0 probability. (THis is not the case)