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Chapter 5: Q T5.8. (page 337)

For events A and B related to the same chance process, which of the following statements is true?

(a) If A and B are mutually exclusive, then they must be independent.

(b) If A and B are independent, then they must be mutually exclusive.

(c) If A and B are not mutually exclusive, then they must be independent.

(d) If A and B are not independent, then they must be mutually exclusive.

(e) If A and B are independent, then they cannot be mutually exclusive.

Short Answer

Expert verified

The correct option is (e)

Step by step solution

01

Step 1. Given

There are two events that are related to the same chance process.

02

Step 2. Concept

A and B are independent, then they cannot be mutually exclusive.

03

Step 3. Explanation

Two events occur as a result of the same random process.

Two occurrences are considered independent if the occurrence of one does not affect the occurrence of the other. Furthermore, two mutually exclusive occurrences cannot be predicted to occur at the same moment. As a result, the independent events are unable to be mutually exclusive.

As a result, the correct option is (e).

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