Question

Suppose that A, B, C are three events that cannot all occur simultaneously. Does this condition necessarily imply that A, B, and C are mutually exclusive ? Justify your answer and illustrate it with a venn diagram.

Short answer

$A$, $B$, and $C$are not always mutually exclusive events. In this situation, the Venn diagram of $A$, $B$, and $C$is as follows:

Step-by-step solution

Step 1. Given information. 

Three occasions $A$, $B$ and $C$ are three separate occurrences that cannot occur at the same time.

Step 2. A, B and C cannot occur simultaneously

If $A$, $B$, and $C$cannot all happen at the same time. Its mean that

$A\cap B\cap C=\varphi$

However, the sentence gives no indication that any two of them have similar results. As a result, $A$, $B$, and $C$are not mutually exclusive. In this situation, the Venn diagram of $A$, $B$, and $C$is as follows