Math Quiz for Music Students
(From conductor Gary Berkson, Stockholm)
- 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.
- 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?
- 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?
- 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 Horace can avoid hearing a single work by Mozart, Beethoven
or Brahms in the next ten years?
- 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?
- 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?
- 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?
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