Suppose there is no outcome common to all three of the events A, B, and C.

Are these three events necessarily mutually exclusive? If your answer is yes, explain why; if your answer is no, give a counter example using the experiment above.

Yes, the event are mutually exclusive ...

Step-by-step explanation:

Event are mutually exclusive if those event cannot occur at the same time. That is the definition of mutually exclusive for instance in a football match, a certain team canot score 0 and 2goals in a match, it is either he scored 2goals or zero goals ... In a throw of a coin we cannot have head and tail at the same time, it is either we have a head or a tail, all the event are mutually exclusive.

Now if we have a dealer selling blue car and two doors car. Let say 20% are blue and 10% have two doors. Then, this are not mutually exclusive because we can have a car that is blue and have two doors.

Mutually exclusive events are like disjoint set in SET theory, where A intersection B intersection C is equal to empty set.

Where A n B n C = {} empty set