Chapter 5: Q 5.73. (page 211)

Let A and B be events of a sample space.
Part (a) Suppose that A and (not B) are mutually exclusive. Explain why B occurs when A occurs.
Part (b) Suppose that B occurs whenever A occurs Explain why A and (not B) are mutually exclusive.

Short Answer

Expert verified

Part (a). $A a n d (n o t B)$ are opposed to each other. It means that if $A$ occurs, $B$ does not, and vice versa. As a result, $B$ occurs everytime $A$ does.

If $A$ occurs, then $B$ occurs, i.e. $(n o t B)$ does not occurs. As a result, $A a n d (n o t B)$ occur it happens at the same time. As a result, they are mutually exclusive.

Step by step solution

Part (a) Step 1. Given information.

Let $A$ and $B$ be sample space events. Let's pretend they're mutually exclusive.

Part (a) Step 2. Calculation.

$A a n d (n o t B)$ are opposed to each other. It means that if $A$ occurs, $B$ does not, and vice versa. As a result, $B$ occurs everytime $A$ does.

Part (b) Step 1. Given information.

Let $A$ and $B$ be sample space events. Assume that $B$ occurs at the same time as $A$ .

Part (b) Step 2. Calculation.

If $A$ occurs, then $B$ occurs, i.e. localid="1651140056335" $(n o t B)$ does not occurs. As a result,localid="1651140065800" $A a n d (n o t B)$ occur it happens at the same time. As a result, they are mutually exclusive.

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Let A and B be events of a sample space.
Part (a) Suppose that A and (not B) are mutually exclusive. Explain why B occurs when A occurs.
Part (b) Suppose that B occurs whenever A occurs Explain why A and (not B) are mutually exclusive.

Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (a) Step 2. Calculation.

Part (b) Step 1. Given information.

Part (b) Step 2. Calculation.

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Let A and B be events of a sample space.Part (a) Suppose that A and (not B) are mutually exclusive. Explain why B occurs when A occurs.Part (b) Suppose that B occurs whenever A occurs Explain why A and (not B) are mutually exclusive.

Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (a) Step 2. Calculation.

Part (b) Step 1. Given information.

Part (b) Step 2. Calculation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Applied Mathematics

Geometry

Logic and Functions

Calculus

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Let A and B be events of a sample space.
Part (a) Suppose that A and (not B) are mutually exclusive. Explain why B occurs when A occurs.
Part (b) Suppose that B occurs whenever A occurs Explain why A and (not B) are mutually exclusive.