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Chapter 5: Q. 5.67. (page 211)

Dice. Refer to exercise 5.53.

a Are events A and B mutually exclusive?

b Are events B and C mutually exclusive?

c Are events A, C and D mutually exclusive?

d Are there three mutually exclusive events among A, B, C and D? four?

Short Answer

Expert verified

Part (a) A and B are not mutually exclusive because they have similar consequences.

Part (b) B and C are mutually exclusive.

Part (c) A, C, and D are not mutually exclusive

Part (d) A,B, C, and D are not mutually exclusive

Step by step solution

01

Part (a) Step 1. Given information.

A = {2,4,6}

B = {4,5,6}

C = {1,2}

D = {3}

02

Part (a) Step 2. A and B are not mutually exclusive events.

A and B are not mutually exclusive because they have similar consequences.

(A鈭�B)={4,6}

03

Part (b) Step 1. Events B and C are mutually exclusive 

Because they have no common outcomes, the occurrences B and C are mutually exclusive.

(B鈭�C)=蠒

04

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

The occurrences A, C, and D are not mutually exclusive because they have similar results.

(A鈭�C)=2

05

 Part (d) Step 1.The events A, B, C, and D are mutually exclusive in three or four ways.

There are three mutually exclusive events among the occurrences A, B, C, and D because no two of them have the same outcome.

Events A, B, C, and D are not mutually exclusive because a pair of them have the same outcome.

(A鈭�B)={4,6},(B鈭�C)=蠒,(C鈭�D)=蠒,(A鈭�B)={4,6},(B鈭�C)=蠒(C鈭�D)=蠒(A鈭�C)={2},(A鈭�D)=蠒,(B鈭�D)=蠒,(A鈭�C)={2},(A鈭�D)=蠒(B鈭�D)=蠒

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