Probability Exam Questions with Solutions by Henk Tijms1

Total Page:16

File Type:pdf, Size:1020Kb

Probability Exam Questions with Solutions by Henk Tijms1 Probability Exam Questions with Solutions by Henk Tijms1 December 15, 2013 This note gives a large number of exam problems for a first course in prob- ability. Fully worked-out solutions of these problems are also given, but of course you should first try to solve the problems on your own! c 2013 by Henk Tijms, Vrije University, Amsterdam. All rights reserved. Per- mission is hereby given to freely print and circulate copies of these notes so long as the notes are not reproduced for commercial purposes. Comments are welcome on [email protected]. 1The exam questions accompany the basic probability material in the chapters 7-14 of my textbook Understanding Probability, third edition, Cambridge University Press, 2012. The simulation-based chapters 1-6 of the book present many probability applications from everyday life to help the beginning student develop a feel for probabilities. Moreover, the book gives an introduction to discrete-time Markov chains and continuous-time Markov chains in the chapters 15 and 16. 1 Chapter 7 7E-1 A bridge hand in which there is no card higher than a nine is called a Yarborough. Specify an appropriate sample space and determine the prob- ability of Yarborough when you are randomly dealt 13 cards out of a well- shuffled deck of 52 cards. 7E-2 Five dots are placed at random on a 8 8 grid in such a way that no × cell contains more than one dot. Specify an appropriate sample space and determine the probability that no row or column contains more than one dot. 7E-3 Five people are sitting at a table in a restaurant. Two of them order coffee and the other three order tea. The waiter forgot who ordered what and puts the drinks in a random order for the five persons. Specify an appropriate sample space and determine the probability that each person gets the correct drink 7E-4 A parking lot has 10 parking spaces arranged in a row. There are 7 cars parked. Assume that each car owner has picked at a random a parking place among the spaces available. Specify an appropriate sample space and determine the probability that the three empty places are adjacent to each other. 7E-5 Somebody is looking for a top-floor apartment. She hears about two vacant apartments in a building with 7 floors en 8 apartments per floor. What is the probability that there is a vacant apartment on the top floor? 7E-6 You choose at random two cards from a standard deck of 52 cards. What is the probability of getting a ten and hearts? 7E-7 A box contains 7 apples and 5 oranges. The pieces of fruit are taken out of the box, one at a time and in a random order. What is the probability that the bowl will be empty after the last apple is taken from the box? 7E-8 A group of five people simultaneously enter an elevator at the ground floor. There are 10 upper floors. The persons choose their exit floors inde- pendently of each other. Specify an appropriate sample space and determine the probability that they are all going to different floors when each person randomly chooses one of the 10 floors as the exit floor. How does the answer 1 change when each person chooses with probability 2 the 10th floor as the exit floor and the other floors remain equally likely as the exit floor with a 1 probability of 18 each. 7E-9 Three friends and seven other people are randomly seated in a row. Specify an appropriate sample space to answer the following two questions. (a) What is the probability that the three friends will sit next to each other? 2 (b) What is the probability that exactly two of the three friends will sit next to each other? 7E-10 You and two of your friends are in a group of 10 people. The group is randomly split up into two groups of 5 people each. Specify an appropriate sample space and determine the probability that you and your two friends are in the same group. 7E-11 You are dealt a hand of four cards from a well-shuffled deck of 52 cards. Specify an appropriate sample space and determine the probability that you receive the four cards J, Q, K, A in any order, with suit irrelevant. 7E-12 You draw at random five cards from a standard deck of 52 cards. What is the probability that there is an ace among the five cards and a king or queen? 7E-13 Three balls are randomly dropped into three boxes, where any ball is equally likely to fall into each box. Specify an appropriate sample space and determine the probability that exactly one box will be empty. 7E-14 An electronic system has four components labeled as 1, 2, 3, and 4. The system has to be used during a given time period. The probability that component i will fail during that time period is fi for i = 1,..., 4. Failures of the components are physically independent of each other. A system failure occurs if component 1 fails or if at least two of the other components fail. Specify an appropriate sample space and determine the probability of a system failure. 7E-15 The Manhattan distance of a point (x, y) in the plane to the origin (0, 0) is defined as x + y . You choose at random a point in the unit square (x, y):0 x, y |1| . What| | is the probability that the Manhattan distance of{ this point≤ to the≤ point} (0, 0) is no more than a for 0 a 2? ≤ ≤ 7E-16 You choose at random a point inside a rectangle whose sides have the lengths 2 and 3. What is the probability that the distance of the point to the closest side of the rectangle is no more than a given value a with 0 <a< 1? 7E-17 Pete tosses n + 1 fair coins and John tosses n fair coins. What is the probability that Pete gets more heads than John? Answer this question first for the cases n = 1 and n = 2 before solving the general case. 7E-18 Bill and Mark take turns picking a ball at random from a bag con- taining four red balls and seven white balls. The balls are drawn out of the bag without replacement and Mark is the first person to start. What is the probability that Bill is the first person to pick a red ball? 3 7E-19 Three desperados A, B and C play Russian roulette in which they take turns pulling the trigger of a six-cylinder revolver loaded with one bullet. Each time the magazine is spun to randomly select a new cylinder to fire as long the deadly shot has not fallen. The desperados shoot according to the order A,B,C,A,B,C,.... Determine for each of the three desperados the probability that this desperado will be the one to shoot himself dead. 7E-20 A fair coin is tossed 20 times. The probability of getting the three or more heads in a row is 0.7870 and the probability of getting three or more heads in a row or three or more tails in a row is 0.9791.2 What is the probability of getting three or more heads in a row and three or more tails in a row? 7E-21 The probability that a visit to a particular car dealer results in neither buying a second-hand car nor a Japanese car is 55%. Of those coming to the dealer, 25% buy a second-hand car and 30% buy a Japanese car. What is the probability that a visit leads to buying a second-hand Japanese car? 7E-22 A fair die is repeatedly rolled and accumulating counts of 1s, 2s, ..., 6s are recorded. What is an upper bound for the probability that the six accumulating counts will ever be equal? 7E-23 A fair die is rolled six times. What is the probability that the largest number rolled is r for r =1,..., 6? 7E-24 Mr. Fermat and Mr. Pascal are playing a game of chance in a cafe in Paris. The first to win a total of ten games is the overall winner. Each 1 of the two players has the same probability of 2 to win any given game. Suddenly the competition is interrupted and must be ended. This happens at a moment that Fermat has won a games and Pascal has won b games with a < 10 and b < 10. What is the probability that Fermat would have been the overall winner when the competition would not have been interrupted? Hint: imagine that another 10 a+10 b 1 games would have been played. − − − 7E-25 A random number is repeatedly drawn from 1, 2,..., 10. What is the probability that not all of the numbers 1, 2,..., 10 show up in 50 drawings? 7E-26 Three couples attend a dinner. Each of the six people chooses ran- domly a seat at a round table. What is the probability that no couple sits together? 7E-27 You roll a fair die six times. What is the probability that three of the six possible outcomes do not show up and each of the other three possible 2These probabilities can be computed by using an absorbing Markov chain discussed in Chapter 15 of the book. 4 outcomes shows up two times? What is the probability that some outcome shows up at least three times? 7E-28 In a group of n boys and n girls, each boy chooses at random a girl and each girl chooses at random a boy.
Recommended publications
  • FORCE IT FACE IT HOPE Handout
    FORCE IT --> HURT FACE IT --> HOPE My soul faints with longing for your salvation, ! I fear scarcity. I believe that God will provide. but I have put my hope in your word.! Psalm 119:81 Show me your ways, O LORD, teach me your paths; ! guide me in your truth and teach me, for you are God ! I say “yes” to myself. I say “yes” to God. my Savior, and my hope is in you all day long. ! Psalm 25:4-5 I ask “Why is this happening to I take the question “Why is Why are you downcast, O my soul? Why so disturbed within me? Put your hope in God, for I will yet praise him, ! me” to the point of narcissistic this happening to me” directly my Savior and my God.! martyrdom and despair. to God. Psalm 42:5 For I know the plans I have for you," declares the LORD, I ignore, mis-use, and/or withhold I accept God’s answer and "plans to prosper you and not to harm you, ! the answer given by God. trust Him to know best. plans to give you hope and a future.! Jeremiah 29:11 The LORD delights in those who fear him, ! I pick favorites. I love unconditionally. who put their hope in his unfailing love.! Psalm 147:11 Though he slay me, yet will I hope in him; ! I choose to stay in my comfort I accept challenges that will I will surely defend my ways to his face.! zone. help me grow and change. Job 13:15 The Lord is good to those whose hope is in him, ! I take matters into my own I take my problems to God to the one who seeks him; ! hands.
    [Show full text]
  • Buffy's Glory, Angel's Jasmine, Blood Magic, and Name Magic
    Please do not remove this page Giving Evil a Name: Buffy's Glory, Angel's Jasmine, Blood Magic, and Name Magic Croft, Janet Brennan https://scholarship.libraries.rutgers.edu/discovery/delivery/01RUT_INST:ResearchRepository/12643454990004646?l#13643522530004646 Croft, J. B. (2015). Giving Evil a Name: Buffy’s Glory, Angel’s Jasmine, Blood Magic, and Name Magic. Slayage: The Journal of the Joss Whedon Studies Association, 12(2). https://doi.org/10.7282/T3FF3V1J This work is protected by copyright. You are free to use this resource, with proper attribution, for research and educational purposes. Other uses, such as reproduction or publication, may require the permission of the copyright holder. Downloaded On 2021/10/02 09:39:58 -0400 Janet Brennan Croft1 Giving Evil a Name: Buffy’s Glory, Angel’s Jasmine, Blood Magic, and Name Magic “It’s about power. Who’s got it. Who knows how to use it.” (“Lessons” 7.1) “I would suggest, then, that the monsters are not an inexplicable blunder of taste; they are essential, fundamentally allied to the underlying ideas of the poem …” (J.R.R. Tolkien, “Beowulf: The Monsters and the Critics”) Introduction: Names and Blood in the Buffyverse [1] In Joss Whedon’s Buffy the Vampire Slayer (1997-2003) and Angel (1999- 2004), words are not something to be taken lightly. A word read out of place can set a book on fire (“Superstar” 4.17) or send a person to a hell dimension (“Belonging” A2.19); a poorly performed spell can turn mortal enemies into soppy lovebirds (“Something Blue” 4.9); a word in a prophecy might mean “to live” or “to die” or both (“To Shanshu in L.A.” A1.22).
    [Show full text]
  • Living Clean the Journey Continues
    Living Clean The Journey Continues Approval Draft for Decision @ WSC 2012 Living Clean Approval Draft Copyright © 2011 by Narcotics Anonymous World Services, Inc. All rights reserved World Service Office PO Box 9999 Van Nuys, CA 91409 T 1/818.773.9999 F 1/818.700.0700 www.na.org WSO Catalog Item No. 9146 Living Clean Approval Draft for Decision @ WSC 2012 Table of Contents Preface ......................................................................................................................... 7 Chapter One Living Clean .................................................................................................................. 9 NA offers us a path, a process, and a way of life. The work and rewards of recovery are never-ending. We continue to grow and learn no matter where we are on the journey, and more is revealed to us as we go forward. Finding the spark that makes our recovery an ongoing, rewarding, and exciting journey requires active change in our ideas and attitudes. For many of us, this is a shift from desperation to passion. Keys to Freedom ......................................................................................................................... 10 Growing Pains .............................................................................................................................. 12 A Vision of Hope ......................................................................................................................... 15 Desperation to Passion ..............................................................................................................
    [Show full text]
  • United States District Court Central District Of
    Case2:85-cv-04544-DMG-AGRDocument1161-1 Filed08/09/21 Page1 of 31 PageID #:44271 1 C ENTER FOR H UMANR IGHTS & C ONSTITUTIONALL AW 2 Carlos R. Holguín (90754) 256 South Occidental Boulevard 3 Los Angeles, CA 90057 4 Telephone: (213) 388-8693 Email: [email protected] 5 6 Attorneys for Plaintiffs 7 Additionalcounsellistedon followingpage 8 9 10 11 UNITEDSTATES DISTRICT COURT 12 CENTRAL DISTRICT OF CALIFORNIA 13 WESTERN DIVISION 14 15 JENNY LISETTE FLORES, et al., No. CV 85-4544-DMG-AGRx 16 Plaintiffs, MEMORANDUM INSUPPORT OF 17 MOTION TO ENFORCE SETTLEMENT REEMERGENCY INTAKE SITES 18 v. Hearing: September 10, 2021 19 M ERRICK G ARLAND, Attorney General of the UnitedStates, et al., Time: 9:30 a.m. 20 Hon. Dolly M. Gee 21 Defendants. 22 23 24 25 26 27 28 1 Case2:85-cv-04544-DMG-AGRDocument1161-1 Filed08/09/21 Page2 of 31 PageID #:44272 1 NATIONALCENTER FOR YOUTHLAW 2 Leecia Welch (Cal. Bar No. 208741) Neha Desai (Cal. RLSA No. 803161) 3 Mishan Wroe (Cal. Bar No. 299296) 4 Melissa Adamson (Cal. Bar No. 319201) Diane de Gramont (Cal. Bar No. 324360) 5 1212 Broadway,Suite 600 Oakland, CA 94612 6 Telephone: (510) 835-8098 Email: [email protected] 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 2 MTE RE EMERGENCY INTAKE SITES CV 85-4544-DMG-AGRX Case2:85-cv-04544-DMG-AGRDocument1161-1 Filed08/09/21 Page3 of 31 PageID #:44273 1 TABLEOF CONTENTS 2 3 4 I.
    [Show full text]
  • The Buffered Slayer: a Search for Meaning in a Secular Age
    Willinger 1 The Buffered Slayer: A Search for Meaning in a Secular Age A Thesis Submitted to The Faculty of the College of Arts and Sciences in Candidacy for the Degree of Master of Arts in English By Kari Willinger 1 May 2018 Willinger 2 Liberty University College of Arts and Sciences Master of Arts in English Student Name: Kari Willinger ______________________________________________________________________________ Dr. Marybeth Baggett, Thesis Chair Date ______________________________________________________________________________ Dr. Stephen Bell, First Reader Date ______________________________________________________________________________ Mr. Alexander Grant, Second Reader Date Willinger 3 Acknowledgments I would like to express my very deep appreciation to: Dr. Baggett, for the encouragement to think outside of the box and patience through the many drafts and revisions; Dr. Bell and Mr. Grant, for providing insightful feedback and direction; My family for prayer and embracing my crazy; My roommates for the endless hours of Buffy marathons; My friends for the continued love and emotional and moral support. You have all challenged and encouraged me through the process of writing this thesis, and I am incredibly grateful to each and every one of you. Willinger 4 Table of Contents Introduction ………………………………………………………………………………………5 Chapter One - The Stakes of Morality: Buffy as Moral Authority …...………….……........15 Chapter Two - Losing Faith: The Buffered Self as Fragmented Identity ……...…..……….29 Chapter Three - The Soulful Undead: Spike’s Dissatisfied Fulfillment ….……….....……..42 Chapter Four - Which Will: A Longing for Enchantment ...…………………………...........56 Conclusion ………………………………………………………………………………………71 Works Cited …………………………………………………………………………….….……77 Willinger 5 Introduction “I knew that everyone I cared about was all right. I knew it. Time ... didn’t mean anything... nothing had form ... but I was still me, you know? And I was warm ..
    [Show full text]
  • Badlands, Blank Space, Border Vacuums, Brown Fields, Conceptual Nevada, Dead Zones …
    10 ISSN: 1755-068 www.field-journal.org vol.1 (1) …badlands, blank space, border vacuums, brown fields, conceptual Nevada, Dead Zones … 1 The term I have used to describe these …badlands, blank space, border vacuums, brown fields, spaces, which is reflected in all the conceptual Nevada, Dead Zones1, derelict areas,ellipsis other terms mentioned above, is ‘dead zone’. The term was taken directly spaces, empty places, free space liminal spaces, from the jargon of urban planners, and from a particular case of such space in ,nameless spaces, No Man’s Lands, polite spaces, , post Tel Aviv (cf. Gil Doron,‘Dead Zones, architectural zones, spaces of indeterminacy, spaces of Outdoor Rooms and the Possibility of Transgressive Urban Space’ in K. Franck uncertainty, smooth spaces, Tabula Rasa, Temporary and Q. Stevens (eds.), Loose Space: Autonomous Zones, terrain vague, urban deserts, Possibility and Diversity in Urban Life (New York: Routledge, 2006). The vacant lands, voids, white areas, Wasteland... SLOAPs term should be read in two ways: one with inverted commas, indicating my Gil M. Doron argument that an area or space cannot be dead or a void, tabula rasa etc. The second reading collapses the term in on itself – while the planners see a dead zone, I argue that it is not the area which If the model is to take every variety of form, then the matter in which the is dead but it is the zone, or zoning, and the assumption that whatever exists model is fashioned will not be duly prepared, unless it is formless, and (even death) in this supposedly delimited free from the impress of any of these shapes which it is hereafter to receive area always transcends the assumed from without.2 boundaries and can be found elsewhere.
    [Show full text]
  • The Empty House by Richard J. Hand the ESTATE
    79 This piece has an accompanying audio file. ANNOUNCER: The Empty House by Richard J. Hand THE ESTATE AGENT IS IN THE LOFT OF AN EMPTY HOUSE. THERE IS BIRDSONG AND TRAFFIC IN BACKGROUND ESTATE AGENT: I’ve been an estate agent for twenty-five years. Sold all kinds of houses. And other properties. Hidden gems and no hopers – I’ve got them on, then swiftly off, the books. I know the language you see, it’s all in the language. I can call a complete dump an opportunity and a punter will buy it – literally. I’ve helped vendors make a mint like that. At the same time, despite my best efforts I’ve seen others let emotion get the better of them and let a place go for a snip. In my experience, empty houses have a sadness to them – a melancholia. Others can brim full of sweet memories. Some almost bleed with lost opportunities or unfounded dreams. I can’t tell you how many times I’ve taken a key and opened the door to an empty house. Stepping over the threshold. An empty house is always lifeless. Didn’t someone once talk of the breathlessness of empty houses? It’s true. Until I went to one particular house. This house. The house I am in now. I’d just gone to measure up. Done it a thousand times. And I always like to talk my way through it. Dictaphone in one hand, tape measure in the other. Type it up later. Used to have cute little cassette tapes.
    [Show full text]
  • Buffy & Angel Watching Order
    Start with: End with: BtVS 11 Welcome to the Hellmouth Angel 41 Deep Down BtVS 11 The Harvest Angel 41 Ground State BtVS 11 Witch Angel 41 The House Always Wins BtVS 11 Teacher's Pet Angel 41 Slouching Toward Bethlehem BtVS 12 Never Kill a Boy on the First Date Angel 42 Supersymmetry BtVS 12 The Pack Angel 42 Spin the Bottle BtVS 12 Angel Angel 42 Apocalypse, Nowish BtVS 12 I, Robot... You, Jane Angel 42 Habeas Corpses BtVS 13 The Puppet Show Angel 43 Long Day's Journey BtVS 13 Nightmares Angel 43 Awakening BtVS 13 Out of Mind, Out of Sight Angel 43 Soulless BtVS 13 Prophecy Girl Angel 44 Calvary Angel 44 Salvage BtVS 21 When She Was Bad Angel 44 Release BtVS 21 Some Assembly Required Angel 44 Orpheus BtVS 21 School Hard Angel 45 Players BtVS 21 Inca Mummy Girl Angel 45 Inside Out BtVS 22 Reptile Boy Angel 45 Shiny Happy People BtVS 22 Halloween Angel 45 The Magic Bullet BtVS 22 Lie to Me Angel 46 Sacrifice BtVS 22 The Dark Age Angel 46 Peace Out BtVS 23 What's My Line, Part One Angel 46 Home BtVS 23 What's My Line, Part Two BtVS 23 Ted BtVS 71 Lessons BtVS 23 Bad Eggs BtVS 71 Beneath You BtVS 24 Surprise BtVS 71 Same Time, Same Place BtVS 24 Innocence BtVS 71 Help BtVS 24 Phases BtVS 72 Selfless BtVS 24 Bewitched, Bothered and Bewildered BtVS 72 Him BtVS 25 Passion BtVS 72 Conversations with Dead People BtVS 25 Killed by Death BtVS 72 Sleeper BtVS 25 I Only Have Eyes for You BtVS 73 Never Leave Me BtVS 25 Go Fish BtVS 73 Bring on the Night BtVS 26 Becoming, Part One BtVS 73 Showtime BtVS 26 Becoming, Part Two BtVS 74 Potential BtVS 74
    [Show full text]
  • Contemporary Worship September 20, 2020 10:30 AM View the Video Stream at Facebook.Com/Mountainviewlv ​
    Contemporary Worship September 20, 2020 10:30 AM View the video stream at facebook.com/mountainviewlv ​ Welcome and Greetings I Am Not Alone When I walk through deep waters I know that You will be with me When I'm standing in the fire I will not be overcome Through the valley of the shadow I will not fear I am not alone, I am not alone You will go before me You will never leave me I am not alone, I am not alone You will go before me You will never leave me In the midst of deep sorrow I see Your light is breaking through The dark of night will not overtake me I am pressing into You Lord You fight my ev'ry battle And I will not fear You amaze me, redeem me You call me as Your own You amaze me, redeem me You call me as Your own You're my strength, You're my defender You're my refuge in the storm Through these trials You've always been faithful You bring healing to my soul © © KAJE Songs (Admin. by EMI Christian Music Publishing), SHOUT! Music Publishing (Admin. by EMI Christian Music Publishing), Worship Together Music (Admin. by EMI Christian Music Publishing), Small City Music (Admin. by Music Services, Inc.), Benjamin Davis Publishing (Admin. by Watershed Music Co.), and Watershed Music Publishing (Admin. by Watershed Music Co.) CCLI Song # 7007821 -- CCLI License # 1944353 By Faith By faith we see the hand of God In the light of creation's grand design In the lives of those who prove His faithfulness Who walk by faith and not by sight By faith our fathers roamed the earth With the pow'r of His promise in their hearts Of a holy city built
    [Show full text]
  • DANGEROUS WOMEN a Thesis Presented to the Graduate Faculty
    DANGEROUS WOMEN A Thesis Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Master of Fine Arts Jana R. Russ August, 2008 DANGEROUS WOMEN Jana R. Russ Thesis Approved: Accepted: _______________________________ _______________________________ Advisor Dean of the College Mary Biddinger Ronald Levant _______________________________ _______________________________ Faculty Reader Dean of the Graduate School Elton Glaser George Newkome _______________________________ _______________________________ Faculty Reader Date Donald Hassler _______________________________ Department Chair Diana Reep ii TABLE OF CONTENTS SECTION I: HOME ................................................................................................................................. 1 Dangerous Women ................................................................................................................ 2 Living in the Hour of the Wolf .............................................................................................. 3 Cream City Bricks ................................................................................................................. 4 Blue Velvet ............................................................................................................................ 6 Flying Free ............................................................................................................................. 7 Letting Go .............................................................................................................................
    [Show full text]
  • Master Engelsk 2007 Morthaugen
    Master Thesis in English Faculty of Humanities Agder University College - Spring 2007 Between Good and Evil On the Moral Ambiguity in ÇBuffy the Vampire SlayerÈ Gro Joanna Morthaugen Gro Joanna Morthaugen Between Good and Evil: On the Moral Ambiguity in Buffy the Vampire Slayer Masteroppgave i Engelsk Høgskolen i Agder Fakultet for Humanistiske Fag 2007 Between Good and Evil: On the Moral Ambiguity in Buffy the Vampire Slayer Gro Joanna Morthaugen Høgskolen i Agder 2007 2 Abstract Gro Joanna Morthaugen Between Good and Evil: On the Moral Ambiguity in Buffy the Vampire Slayer Mastergradsoppgave ved Institutt for engelsk Høgskolen i Agder Vår 2007 Joss Whedon’s Buffy the Vampire Slayer aims to empower young women through a declared feminist agenda. The main body of this thesis explores what it is that makes Buffy a television show with a feminist agenda. This thesis analyzes areas which privileges and problematizes human agency from the perspective morals in society. The series advocates using one’s agency in order to optimize potentiality. The thesis examines emotions and human agency; manslaughter and notions of the Übermensch, and finally, the claim of agency and consequent empowerment of women. I have found that several aspects of the series problematize moral choices and privilege and a feminist agenda, with the tenets of qualified "girl power" / third way feminism leading to an alternative notion of feminine empowerment. Maintaining that Buffy is not purely entertainment, it also comments on the present state of society, with its moral ambiguities and wavering of feminism. Since this is a popular phenomenon which borrows freely from aspects of popular culture, the theoretical concepts of feminism, power, emotions, and Kant’s moral agent have been qualified.
    [Show full text]
  • The Rev. James Richardson 7 Easter: Ascension Sunday June 2, 2019 A
    The Rev. James Richardson 7 Easter: Ascension Sunday June 2, 2019 A couple of months ago, Lori and I attended a conference that featured speakers on a wide range of topics mostly out of my wheelhouse. One of the most fascinating – and mystifying – was titled “The Space-Time Symphony,” by a professor from Sonoma State University, Lynn Cominsky, who is an astrophysicist. Professor Cominsky is one of 1,500 scientists worldwide working on a project called LIGO, which stands for the Laser Interferometer Gravitational-Wave Observatory. I cannot possibly explain what all of those words mean or how this works. The math is way beyond me – this is all Einstein Relativity stuff. But go with me here for a few minutes. We might look out into space and think of it as a vast void of empty darkness, but the scientists at LIGO will tell you it is anything but empty. What these scientists are doing is measuring the ripples in space and time created by gravity from massive objects like black holes. They are able to detect the final moments of neutron stars and black holes colliding. For fun, they convert these gravitational waves into sound, hence the title of Professor Cominsky’s talk, “The Space-Time Symphony.” Astrophysicists are easily amused. So where am I going with this? This morning is called “Ascension Sunday,” marking the moment when Jesus disappears from his disciples. We observe this day last Thursday, and we continue to observe this until next Sunday. So, what is the Ascension? Jesus has gone to his death on the Cross, and on the third day, he has risen from the grave.
    [Show full text]