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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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Most popular questions from this chapter

In each of Exercises 5.167-5.172, we have provided the number of trials and success probability for Bernoulli trials. LetX denote the total number of successes. Determine the required probabilities by using

(a) the binomial probability formula, Formula 5.4 on page 236. Round your probability answers to three decimal places.

(b) TableVII in AppendixA. Compare your answer here to that in part (a).

n=4,p=14,P(X=2)

Housing Units. Refer to Exercise 5.19.

(a) Which, if any, of the events in parts (a)-(c) are certain? impossible?

(b). Determine the probability of each event identified in part (a).

For each of the following probability histograms of binomial distributions, specify whether the success probability is less than, equal to, or greater than 0.5. Explain your answers.

Identify a commonly used graphical technique for portraying events and relationships among events.

Concerning the equal-likelihood model of probability,

(a). what is it?

(b). how is the probability of an event found?
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