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Chapter 5: Q 5.75. (page 211)

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

Expert verified

A, B, and Care not always mutually exclusive events. In this situation, the Venn diagram of A, B, and Cis as follows:

Step by step solution

01

Step 1. Given information. 

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

02

Step 2. A, B and C cannot occur simultaneously

If A, B, and Ccannot all happen at the same time. Its mean that

A∩B∩C=ϕ

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

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