To determine Find the probability that a woman has the disease given that she have taken the test and received a favorable result. Explanation Calculation: Bayes’ Rule: Let B 1 , B 2 , ... , B k constitute a partition of the sample space S such that P ( B i ) ≠ 0 for i = 1 , 2 , … , k , then for any event A of S such that P ( A ) ≠ 0 , P ( B r | A ) = P ( B r ) P ( A | B r ) ∑ i = 1 k P ( B i ) P ( A | B i ) for r = 1 , 2 , … , k . Let event C is defined as that a woman over 60 has the cancer, event P is defined as that the test gives a positive result, event C’ is defined as that a woman over 60 has no cancer, and event P’ is defined as that the test gives a negative result. The probability that a woman over 60 has the cancer is 0.07. That is, P ( C ) = 0.07 , then the probability that a woman over 60 has no cancer is 0.93. That is, P ( C ' ) = 0.93 , the probability that the test gives negative results given that woman over 60 has the cancer is 0.10. That is, P ( P ' | C ) = 0

Probability & Statistics for Engineers & Scientists, MyLab Statistics Update (9th Edition)

9th Edition

ISBN: 9780134115856

Author: Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, Keying E. Ye

Publisher: PEARSON

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Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of …

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Chapter 2.7, Problem 118RE

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Find the probability that a woman has the disease given that she have taken the test and received a favorable result.

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Chapter 2.7, Problem 117RE

Chapter 2.7, Problem 119RE

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Chapter 2 Solutions

Probability & Statistics for Engineers & Scientists, MyLab Statistics Update (9th Edition)

Ch. 2.2 - List the elements of each of the following sample...Ch. 2.2 - Use the rule method to describe the sample space S...Ch. 2.2 - Which of the following events are equal? A = {1,...Ch. 2.2 - An experiment involves tossing a pair of dice, one...Ch. 2.2 - Prob. 5E Ch. 2.2 - Two jurors are selected from 4 alternates to serve...Ch. 2.2 - Prob. 7E Ch. 2.2 - For the sample space of Exercise 2.4, list the...Ch. 2.2 - Prob. 9E Ch. 2.2 - Prob. 10E

Ch. 2.2 - Prob. 11E Ch. 2.2 - Exercise and diet are being studied as possible...Ch. 2.2 - Prob. 13E Ch. 2.2 - Prob. 14E Ch. 2.2 - Consider the sample space S = {copper, sodium,...Ch. 2.2 - If S = {x | 0 < x < 12}, M = {x | 1 < x < 9}, and...Ch. 2.2 - Prob. 17E Ch. 2.2 - Which of the following pairs of events are...Ch. 2.2 - Prob. 19E Ch. 2.2 - Referring to Exercise 2.19 and the Venn diagram of...Ch. 2.3 - Registrants at a large convention are offered 6...Ch. 2.3 - In a medical study, patients are classified in 8...Ch. 2.3 - Prob. 23E Ch. 2.3 - Students at a private liberal arts college are...Ch. 2.3 - A certain brand of shoes comes in 5 different...Ch. 2.3 - Prob. 26E Ch. 2.3 - Prob. 27E Ch. 2.3 - A drug for the relief of asthma can be purchased...Ch. 2.3 - Prob. 29E Ch. 2.3 - In how many different ways can a true-false...Ch. 2.3 - A witness to a hit-and-run accident told the...Ch. 2.3 - In how many ways can 6 people be lined upto get on...Ch. 2.3 - If a multiple-choice test consists of 5 questions,...Ch. 2.3 - Prob. 34E Ch. 2.3 - Prob. 35E Ch. 2.3 - Prob. 36E Ch. 2.3 - Prob. 37E Ch. 2.3 - Prob. 38E Ch. 2.3 - In a regional spelling bee, the 8 finalists...Ch. 2.3 - In how many ways can 5 starting positions on a...Ch. 2.3 - Find the number of ways that 6 teachers can be...Ch. 2.3 - Prob. 42E Ch. 2.3 - Prob. 43E Ch. 2.3 - In how many ways can a caravan of 8 covered wagons...Ch. 2.3 - Prob. 45E Ch. 2.3 - In how many ways can 3 oaks, 4 pines, and 2 maples...Ch. 2.3 - How many ways are there to select 3 candidates...Ch. 2.3 - How many ways are there that no two students will...Ch. 2.5 - Find the errors in each of the following...Ch. 2.5 - Prob. 50E Ch. 2.5 - A box contains 500 envelopes, of which 75...Ch. 2.5 - Suppose that in a senior college class of 500...Ch. 2.5 - The probability that an American industry will...Ch. 2.5 - From past experience, a stockbroker believes that...Ch. 2.5 - If each coded item in a catalog begins with 3...Ch. 2.5 - An automobile manufacturer is concerned about a...Ch. 2.5 - Prob. 57E Ch. 2.5 - A pair of fair dice is tossed. Find the...Ch. 2.5 - In a poker hand consisting of 5 cards, find the...Ch. 2.5 - If 3 books are picked at random from a shelf...Ch. 2.5 - In a high school graduating class of 100 students,...Ch. 2.5 - Prob. 62E Ch. 2.5 - Prob. 63E Ch. 2.5 - Interest centers around the life of an electronic...Ch. 2.5 - Prob. 65E Ch. 2.5 - Factory workers are constantly encouraged to...Ch. 2.5 - Consider the situation of Example 2.32 on page...Ch. 2.5 - Interest centers around the nature of an oven...Ch. 2.5 - Prob. 69E Ch. 2.5 - Prob. 70E Ch. 2.5 - As the situation of Exercise 2.69 might suggest,...Ch. 2.5 - Prove that P(A′ ∩ B′) = 1+P(A ∩ B) − P(A) − P(B). Ch. 2.6 - If R is the event that a convict committed armed...Ch. 2.6 - Prob. 74E Ch. 2.6 - A random sample of 200 adults are classified below...Ch. 2.6 - In an experiment to study the relationship of...Ch. 2.6 - In the senior year of a high school graduating...Ch. 2.6 - A manufacturer of a flu vaccine is concerned about...Ch. 2.6 - In USA Today (Sept. 5, 1996), the results of a...Ch. 2.6 - Prob. 80E Ch. 2.6 - Prob. 81E Ch. 2.6 - For married couples living in a certain suburb,...Ch. 2.6 - The probability that a vehicle entering the Luray...Ch. 2.6 - The probability that the head of a household is...Ch. 2.6 - The probability that a doctor correctly diagnoses...Ch. 2.6 - In 1970, 11% of Americans completed four years of...Ch. 2.6 - A real estate agent has 8 master keys to open...Ch. 2.6 - Before the distribution of certain statistical...Ch. 2.6 - A town has two fire engines operating...Ch. 2.6 - Prob. 90E Ch. 2.6 - Find the probability of randomly selecting 4 good...Ch. 2.6 - Prob. 92E Ch. 2.6 - A circuit system is given in Figure 2.11. Assume...Ch. 2.6 - Prob. 94E Ch. 2.7 - In a certain region of the country it is known...Ch. 2.7 - Police plan to enforce speed limits by using...Ch. 2.7 - Referring to Exercise 2.95, what is the...Ch. 2.7 - If the person in Exercise 2.96 received a speeding...Ch. 2.7 - Suppose that the four inspectors at a film factory...Ch. 2.7 - A regional telephone company operates three...Ch. 2.7 - A paint-store chain produces and sells latex and...Ch. 2.7 - Prob. 102E Ch. 2.7 - Prob. 103RE Ch. 2.7 - An allergist claims that 50% of the patients she...Ch. 2.7 - Prob. 105RE Ch. 2.7 - Prob. 106RE Ch. 2.7 - Prob. 107RE Ch. 2.7 - Prob. 108RE Ch. 2.7 - A large industrial firm uses three local motels to...Ch. 2.7 - The probability that a patient recovers from a...Ch. 2.7 - Prob. 111RE Ch. 2.7 - Prob. 112RE Ch. 2.7 - Prob. 113RE Ch. 2.7 - Prob. 114RE Ch. 2.7 - A certain federal agency employs three consulting...Ch. 2.7 - A manufacturer is studying the effects of cooking...Ch. 2.7 - Prob. 117RE Ch. 2.7 - A certain form of cancer is known to be found in...Ch. 2.7 - A producer of a certain type of electronic...Ch. 2.7 - Prob. 120RE Ch. 2.7 - Prob. 121RE Ch. 2.7 - Prob. 122RE Ch. 2.7 - Prob. 123RE Ch. 2.7 - Prob. 124RE Ch. 2.7 - A survey of those using a particular statistical...Ch. 2.7 - During bad economic times, industrial workers are...Ch. 2.7 - There is a 50-50 chance that the queen carries the...

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