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Chapter 5: Q. 5.68. (page 211)

Horse racing. Each part of this exercise contains events from Exercise 5.54. In each case, decide whether the event are mutually exclusive.

Part (a) A and B

Part (a) B and C

Part (a) A, B and C

Part (a) A,B and D

Part (a) A, B, C and D

Short Answer

Expert verified

Part (a) The events A and B are mutually exclusive

Part (b) The events B and C are mutually exclusive

Part (c) The events A,B and C are not mutually exclusive

Part (d) The events A,B and D are mutually exclusive

Part (e) The events A,B,C and D are not mutually exclusive

Step by step solution

01

Part (a) Step 1. Given information.

A={3,4}B={6,7,8}C={1,2,3}D={2,5}

02

Part (a) Step 2., The events A and B are mutually exclusive 

Because they have no shared outcomes, events A and B are mutually exclusive.

A∩B=ϕ

03

Part (b) Step 1., The events B and C are mutually exclusive 

Because they have no shared outcomes, events B and C are mutually exclusive.

B∩C=ϕ

04

Part (c) Step 1., A, B, and C are not mutually exclusive.

A, B, and C are not mutually exclusive. Because there are two of them with similar results, they are mutually exclusive.

A∩C=3

05

Part (d) Step 1. A, B, and D are mutually exclusive events.

A∩B=ϕB∩D=ϕA∩D=ϕ

Therefore, A, B, and D are mutually exclusive events.

06

Part (d) Step 1. A, B, C, and D are not mutually exclusive events.

A∩C=3

Therefore A, B, C, and D are not mutually exclusive events.

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Most popular questions from this chapter

In Exercises 5.16-5.26, express your probability answers as a decimal rounded to three places.

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