Mathematics for Musicians



    1. Wilma is tired of paying for clarinet reeds. If she adopts a
       policy of playing only on rejected reeds from her colleagues will
       she be able to retire on the money she has saved if she invests it
       in mutual bonds, yielding 8.7%, before she is fired from her job?
       If not, calculate the probability of her ever working in a
       professional symphony orchestra again.
       
    2. Jethro has been playing the double bass in a symphony orchestra
       for twelve years, three months and seven days. Each day, his
       inclination to practice decreases by the equation:
       (Total days in the orchestra) x .000976
       Assuming he stopped practicing altogether four years, six months
       and three days ago, how long will it be before he is completely
       unable to play the double bass?
       
    3. Wilma plays in the second violin section, but specializes in
       making disparaging remarks about conductors and other musicians.
       The probability of her making a negative comment about any given
       musician is 4 chances in 7, and for conductors is 16 chances in
       17. If there are 103 musicians in the orchestra and the orchestra
       sees 26 different conductors a year, how many negative comments
       does Wilma make in a two-year period? How does this change if five
       of the musicians are also conductors? What if six of the
       conductors are also musicians?
       
    4. Horace is the General Manager of an important symphony orchestra.
       He tries to hear at least four concerts a year. Assuming that at
       each concert the orchestra plays a minimum of three pieces per
       concert, what are the chances that Horacecan avoid hearing a
       single work by Mozart, Beethoven or Brahms in the next ten years?
       
    5. Betty plays in the viola section. Despite her best efforts she is
       unable to play with the rest of the orchestra and, on average,
       plays .3528 seconds behind the rest of the viola section, which is
       already .16485 seconds behind the rest of the orchestra. If the
       orchestra is moving into a new concert hall with a reverberation
       time of 2.7 seconds, will she be able to continue playing this way
       undetected?
       
    6. Ralph loves to drink coffee. Each week he drinks three more cups
       of coffee than Harold, who drinks exactly one third the amount
       that the entire brass section consumes in beer. How much longer is
       Ralph going to live?
       
    7. Rosemary is unable to play in keys with more than three sharps or
       flats without making an inordinate number of mistakes. Because her
       colleagues in the cello section are also struggling in these
       passages she has so far been able to escape detection. What is the
       total number of hours they would all have to practice to play the
       complete works of Richard Strauss?
       
   Taken from the Amusements Pages of the New Zealand Symphony Orchestra
   






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