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A business office orders paper supplies from one of three

Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer ISBN: 9780495110811 47

Solution for problem 19E Chapter 2

Mathematical Statistics with Applications | 7th Edition

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Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer

Mathematical Statistics with Applications | 7th Edition

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Problem 19E

A business office orders paper supplies from one of three vendors, V1, V2, or V3. Orders are to be placed on two successive days, one order per day. Thus, (V2, V3) might denote that vendor V2 gets the order on the first day and vendor V3 gets the order on the second day.

a List the sample points in this experiment of ordering paper on two successive days.

b Assume the vendors are selected at random each day and assign a probability to each sample point.

c Let A denote the event that the same vendor gets both orders and B the event that V2 gets at least one order. Find P( A), P( B), P( A ∪ B), and P( A ∩ B) by summing the probabilities of the sample points in these events.

Step-by-Step Solution:

Answer:

Step 1 of 3:

Given, V1, V2 and V3 are the 3 vendors, A business office orders paper supplies from one of the three vendor. Orders are to be placed on two successive days and one order per day.

V2 gets the order on the first day and vendor V3 gets the order on the second day.

The claim is to list all sample points in this experiment of ordering paper on two successive days.

Since there is no restriction. One vendor can also supply paper both the days.

Then the sample space is s = {(V1, V1), (V2, V2),  (V3, V3), (V1,V2), (V2, V1), (V1, V3),

                                                     (V3, V1),(V2, V3), (V3, V2) }

Step 2 of 3:

b) the claim is to assign a probability to each sample point.

Probability =

We have 9 possible outcomes and each event in the sample space has equal probability

Then, Probability =

                            = 0.11

Hence, probability to each sample point is 0.11

Step 3 of 3

Chapter 2, Problem 19E is Solved
Textbook: Mathematical Statistics with Applications
Edition: 7
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
ISBN: 9780495110811

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