Question

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.

Answer 1

Yes, the event are mutually exclusive...

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