Question

Hi,
this is from AKSHAY
The question is as follows,
A series with three matches between India and South Africa is about to start. Consider the three events associated with the result of the match.
A.SA wins at least two matches
B.SA wins exactly one match
C.SA wins no match
Statement: The three events A,B and C are mutually exclusive and exhaustive events.

I can understand the answer but except last statement that
A_{​​​​​}​​​​​​ Intersection B is null ,B intersection C is null ,C intersection A is null
How it comes?

Answer 1

A.the first result says that SA wins at least two matches. So from this statement it is clear that SA have to win minimum 2 matches, and it may be 3 matches also. But it is not possible to win 1 match or no match. So this statement is p exclusive from statement B and statement C.

B. The second result says that SA will have to win exactly 1 match. So from this statement it is clear that there is no scope of SA to win at least two matches (statement A) or no match (statement C​​​​​​). SA have to win only or exactly 1 match. So this statement is exclusive from statement A and C.

C. this statement says that SA wins no match. Means there is no scope of SA to win exactly one match or at least 2 matches. So this statement is also exclusive from statement A and B.

So from these explanation that results A, B, and C are mutually exclusive.

​​​​ Exhaustive event is such a event in which atleast one incident among result A, B or C must be happened. And it is true in the case of SA also. SA may win no match. SA may win exactly one match also. And SA may win at least 2 matches also. So these three events are mutually Exhaustive also.

Because of these three events are mutually exclusive and Exhaustive A​​​​ Intersection B is null ,B intersection C is null ,C intersection A is null.