Mathematical Methods in the Physical Sciences
3rd Edition
ISBN: 9780471198260
Author: Mary L. Boas
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 15.3, Problem 15P
Use Bayes' formula ( 3.8 ) to repeat these simple problems previously done by using a reduced
(a) In a family of two children, what is the probability that both are girls if at least one is a girl?
(b) What is the probability of all heads in three tosses of a coin if you know that at least one is a head?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Chapter 15 Solutions
Mathematical Methods in the Physical Sciences
Ch. 15.1 - If you select a three-digit number at random, what...Ch. 15.1 - Three coins are tossed; what is the probability...Ch. 15.1 - In a box there are 2 white, 3 black, and 4 red...Ch. 15.1 - A single card is drawn at random from a shuffled...Ch. 15.1 - Given a family of two children (assume boys and...Ch. 15.1 - A trick deck of cards is printed with the hearts...Ch. 15.1 - A letter is selected at random from the alphabet....Ch. 15.1 - An integer N is chosen at random with 1N100. What...Ch. 15.1 - You are trying to find instrument A in a...Ch. 15.1 - A shopping mall has four entrances, one on the...
Ch. 15.2 - Set up an appropriate sample space for each of...Ch. 15.2 - Set up an appropriate sample space for each of...Ch. 15.2 - Set up an appropriate sample space for each of...Ch. 15.2 - Set up an appropriate sample space for each of...Ch. 15.2 - Set up an appropriate sample space for each of...Ch. 15.2 - Set up an appropriate sample space for each of...Ch. 15.2 - Set up an appropriate sample space for each of...Ch. 15.2 - Set up an appropriate sample space for each of...Ch. 15.2 - Set up an appropriate sample space for each of...Ch. 15.2 - Set up an appropriate sample space for each of...Ch. 15.2 - Set up several nonuniform sample spaces for the...Ch. 15.2 - Use the sample space of Example 1 above, or one or...Ch. 15.2 - A student claims in Problem 1.5 that if one child...Ch. 15.2 - Two dice are thrown. Use the sample space ( 2.4 )...Ch. 15.2 - Use both the sample space (2.4) and the sample...Ch. 15.2 - Given an nonuniform sample space and the...Ch. 15.2 - Two dice are thrown. Given the information that...Ch. 15.2 - Are the following correct nomuniform sample spaces...Ch. 15.2 - Consider the set of all permutations of the...Ch. 15.3 - (a) Set up a sample space for the 5 black and 10...Ch. 15.3 - Prove (3.1) for a nonuniform sample space. Hints:...Ch. 15.3 - What is the probability of getting the sequence...Ch. 15.3 - (a) A weighted coin has probability of 23 of...Ch. 15.3 - What is the probability that a number n,1n99, is...Ch. 15.3 - A card is selected from a shuffled deck. What is...Ch. 15.3 - (a) Note that (3.4) assumes P(A)0 since PA(B) is...Ch. 15.3 - Show that...Ch. 15.3 - Prob. 9PCh. 15.3 - Three typed letters and their envelopes are piled...Ch. 15.3 - In paying a bill by mail, you want to put your...Ch. 15.3 - (a) A loaded die has probabilities...Ch. 15.3 - (a) A candy vending machine is out of order. The...Ch. 15.3 - A basketball player succeeds in making a basket 3...Ch. 15.3 - Use Bayes' formula ( 3.8 ) to repeat these simple...Ch. 15.3 - Suppose you have 3 nickels and 4 dimes in your...Ch. 15.3 - (a) There are 3 red and 5 black balls in one box...Ch. 15.3 - Two cards are drawn at random from a shuffled...Ch. 15.3 - Suppose it is known that 1 of the population have...Ch. 15.3 - Some transistors of two different kinds (call them...Ch. 15.3 - Two people are taking turns tossing a pair of...Ch. 15.3 - Repeat Problem 21 if the players toss a pair of...Ch. 15.3 - A thick coin has 37 probability of falling heads,...Ch. 15.4 - (a) There are 10 chairs in a row and 8 people to...Ch. 15.4 - In the expansion of (a+b)n (see Example 2), let...Ch. 15.4 - A bank allows one person to have only one savings...Ch. 15.4 - Five cards are dealt from a shuffled deck. What is...Ch. 15.4 - A bit (meaning binary digit) is 0 or 1. An ordered...Ch. 15.4 - A so-called 7 -way lamp has three 60 -watt bulbs...Ch. 15.4 - What is the probability that the 2 and 3 of clubs...Ch. 15.4 - Two cards are drawn from a shuffled deck. What is...Ch. 15.4 - Two cards are drawn from a shuffled deck. What is...Ch. 15.4 - What is the probability that you and a friend have...Ch. 15.4 - The following game was being played on a busy...Ch. 15.4 - Consider Problem 10 for different months of birth....Ch. 15.4 - Generalize Example 3 to show that the number of...Ch. 15.4 - (a) Find the probability that in two tosses of a...Ch. 15.4 - Set up the uniform sample spaces for the problem...Ch. 15.4 - Do Problem 15 for 2 particles in 2 boxes. Using...Ch. 15.4 - Find the number of ways of putting 2 particles in...Ch. 15.4 - Find the number of ways of putting 3 particles in...Ch. 15.4 - (a) Following the methods of Examples 3, 4, and 5,...Ch. 15.4 - (a) In Example 5, a mathematical model is...Ch. 15.4 - The following problem arises in quantum mechanics...Ch. 15.4 - Suppose 13 people want to schedule a regular...Ch. 15.4 - Do Problem 22 if one person is busy 3 evenings,...Ch. 15.5 - Set up sample spaces for Problems 1 to 7 and list...Ch. 15.5 - Set up sample spaces for Problems 1 to 7 and list...Ch. 15.5 - Set up sample spaces for Problems 1 to 7 and list...Ch. 15.5 - Set up sample spaces for Problems 1 to 7 and list...Ch. 15.5 - Set up sample spaces for Problems 1 to 7 and list...Ch. 15.5 - Set up sample spaces for Problems 1 to 7 and list...Ch. 15.5 - Set up sample spaces for Problems 1 to 7 and list...Ch. 15.5 - Would you pay $10 per throw of two dice if you...Ch. 15.5 - Prob. 9PCh. 15.5 - Let be the average of the random variable x. Then...Ch. 15.5 - Show that the expected number of heads in a single...Ch. 15.5 - Use Problem 9 to find the expected value of the...Ch. 15.5 - Show that adding a constant K to a random variable...Ch. 15.5 - As in Problem 11, show that the expected number of...Ch. 15.5 - Use Problem 9 to find x in Problem 7.Ch. 15.5 - Show that 2=Ex22. Hint: Write the definition of 2...Ch. 15.5 - Use Problem 16 to find in Problems 2, 6, and 7.Ch. 15.6 - (a) Find the probability density function f(x) for...Ch. 15.6 - It is shown in the kinetic theory of gases that...Ch. 15.6 - A ball is thrown straight up and falls straight...Ch. 15.6 - In Problem 1 we found the probability density...Ch. 15.6 - The probability for a radioactive particle to...Ch. 15.6 - A circular garden bed of radius 1m is to be...Ch. 15.6 - (a) Repeat Problem 6 where the circular area is...Ch. 15.6 - Given that a particle is inside a sphere of radius...Ch. 15.6 - Prob. 9PCh. 15.6 - Do Problem 5.10 for a continuous distribution.Ch. 15.6 - Do Problem 5.13 for a continuous distribution.Ch. 15.6 - Do Problem 5.16 for a continuous distribution.Ch. 15.6 - Prob. 13PCh. 15.6 - Prob. 14PCh. 15.6 - Show that the covariance of two independent (see...Ch. 15.6 - Prob. 16PCh. 15.7 - For the values of n indicated in Problems 1 to 4 :...Ch. 15.7 - For the values of n indicated in Problems 1 to 4:...Ch. 15.7 - For the values of n indicated in Problems 1 to 4:...Ch. 15.7 - For the values of n indicated in Problems 1 to 4:...Ch. 15.7 - Write the formula for the binomial density...Ch. 15.7 - For the given values of n and p in Problems 6 to...Ch. 15.7 - For the given values of n and p in Problems 6 to...Ch. 15.7 - For the given values of n and p in problems 6 to...Ch. 15.7 - Use the second method of Problem 5.11 to show that...Ch. 15.7 - Show that the most probable number of heads in n...Ch. 15.7 - Use the method of Problem 10 to show that for the...Ch. 15.7 - Let x= number of heads in one toss of a coin. What...Ch. 15.7 - Generalize Problem 12 to show that for the general...Ch. 15.8 - Verify that for a random variable x with normal...Ch. 15.8 - Do Problem 6.4 by comparing eax2 with f(x) in...Ch. 15.8 - The probability density function for the x...Ch. 15.8 - Prob. 4PCh. 15.8 - Computer plot on the same axes the normal density...Ch. 15.8 - Do Problem 5 for =16,13,1.Ch. 15.8 - By computer find the value of the normal...Ch. 15.8 - Carry through the following details of a...Ch. 15.8 - Computer plot a graph like Figure 8.3 of the...Ch. 15.8 - Computer plot graphs like Figure 8.2 but with p12...Ch. 15.8 - As in Examples 1 and 2, use (a) the binomial...Ch. 15.8 - As in Examples 1 and 2, use (a) the binomial...Ch. 15.8 - As in Examples 1 and 2, use (a) the binomial...Ch. 15.8 - As in Examples 1 and 2, use (a) the binomial...Ch. 15.8 - As in Examples 1 and 2, use (a) the binomial...Ch. 15.8 - As in Examples 1 and 2, use (a) the binomial...Ch. 15.8 - As in Examples 1 and 2, use (a) the binomial...Ch. 15.8 - As in Examples 1 and 2, use (a) the binomial...Ch. 15.8 - As in Examples 1 and 2, use (a) the binomial...Ch. 15.8 - As in Examples 1 and 2, use (a) the binomial...Ch. 15.8 - As in Examples 1 and 2, use (a) the binomial...Ch. 15.8 - As in Examples 1 and 2, use (a) the binomial...Ch. 15.8 - As in Examples 1 and 2, use (a) the binomial...Ch. 15.8 - As in Examples 1 and 2, use (a) the binomial...Ch. 15.8 - As in Examples 1 and 2, use (a) the binomial...Ch. 15.9 - Solve the sequence of differential equations (9.4)...Ch. 15.9 - Show that the average value of a random variable n...Ch. 15.9 - In an alpha-particle counting experiment the...Ch. 15.9 - Suppose you receive an average of 4 phone calls...Ch. 15.9 - Suppose that you have 5 exams during the 5 days of...Ch. 15.9 - If you receive, on the average, 5 email messages...Ch. 15.9 - In a club with 500 members, what is the...Ch. 15.9 - If there are 100 misprints in a magazine of 40...Ch. 15.9 - If there are, on the average, 7 defects in a new...Ch. 15.9 - Derive equation ( 9.9 ) as follows: In C(n,x),...Ch. 15.9 - Suppose 520 people each have a shuffled deck of...Ch. 15.9 - Computer plot on the same axes graphs of the...Ch. 15.9 - Computer plot on the same axes a graph of the...Ch. 15.10 - Let m1,m2,,mn be a set of measurements, and define...Ch. 15.10 - Let x1,x2,,xn be independent random variables,...Ch. 15.10 - Define s by the equation s2=(1/n)i=1nxix2. Show...Ch. 15.10 - Assuming a normal distribution, find the limits h...Ch. 15.10 - Show that if w=xy or w=x/y, then ( 10.14) gives...Ch. 15.10 - By expanding w(x,y,z) in a three-variable power...Ch. 15.10 - Prob. 7PCh. 15.10 - The following measurements of x and y have been...Ch. 15.10 - Given the measurements...Ch. 15.10 - Given the measurements...Ch. 15.11 - (a) Suppose you have two quarters and a dime in...Ch. 15.11 - (a) Suppose that Martian dice are regular...Ch. 15.11 - There are 3 red and 2 white balls in one box and 4...Ch. 15.11 - If 4 letters are put at random into 4 envelopes,...Ch. 15.11 - Two decks of cards are matched, that is, the order...Ch. 15.11 - Find the number of ways of putting 2 particles in...Ch. 15.11 - Suppose a coin is tossed three times. Let x be a...Ch. 15.11 - (a) A weighted coin has probability 23 of coming...Ch. 15.11 - One box contains one die and another box contains...Ch. 15.11 - Do Problems 10 to 12 using both the binomial...Ch. 15.11 - Do Problems 10 to 12 using both the binomial...Ch. 15.11 - Do Problems 10 to 12 using both the binomial...Ch. 15.11 - A radioactive source emits 1800 particles during...Ch. 15.11 - Suppose a 200-page book has, on the average, one...Ch. 15.11 - In Problems 15 and 16, find the binomial...Ch. 15.11 - In Problems 15 and 16, find the binomial...Ch. 15.11 - Given the measurements...Ch. 15.11 - Given the measurements...
Additional Math Textbook Solutions
Find more solutions based on key concepts
(see the Student Project). This definition is used to solve some important initial-value problems in differenti...
Calculus Volume 2
In Exercises 1–6, fill in the blanks with an appropriate word, phrase, or symbol(s).
1. When the conclusion of...
A Survey of Mathematics with Applications (10th Edition) - Standalone book
Percentiles. The pth percentile of a sorted data set is a number xp such that p of the data fall at or below xp...
Excursions in Modern Mathematics (9th Edition)
In each of Problems 2 through 9, find the general solution of the given system. Calculations are greatly facili...
Differential Equations: An Introduction to Modern Methods and Applications
Checkpoint1
Use the substitution method to solve this system:
Answers to Checkpoint exercises are found at the...
Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
Find the additive inverse of each of the following integers. Write the answer in the simplest possible form. a....
A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- If a binomial experiment has probability p success, then the probability of failure is ____________________. The probability of getting exactly r successes in n trials of this experiment is C(_________, _________)p (1p)arrow_forwardIn Example 8, what is the probability that an employee chosen at random has 30 or more years of service?arrow_forwardFlexible Work Hours In a recent survey, people were asked whether they would prefer to work flexible hours----even when it meant slower career advancement----so they could spend more time with their families. The figure shows the results of the survey. What is the probability that three people chosen at random would prefer flexible work hours?arrow_forward
Recommended textbooks for you
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Statistics 4.1 Point Estimators; Author: Dr. Jack L. Jackson II;https://www.youtube.com/watch?v=2MrI0J8XCEE;License: Standard YouTube License, CC-BY
Statistics 101: Point Estimators; Author: Brandon Foltz;https://www.youtube.com/watch?v=4v41z3HwLaM;License: Standard YouTube License, CC-BY
Central limit theorem; Author: 365 Data Science;https://www.youtube.com/watch?v=b5xQmk9veZ4;License: Standard YouTube License, CC-BY
Point Estimate Definition & Example; Author: Prof. Essa;https://www.youtube.com/watch?v=OTVwtvQmSn0;License: Standard Youtube License
Point Estimation; Author: Vamsidhar Ambatipudi;https://www.youtube.com/watch?v=flqhlM2bZWc;License: Standard Youtube License