A radio station that plays classical music has a "By Request" program each Saturday night. The percentage of requests for composers on a particular night are listed below:
Composers Percentage of Requests
Bach 5
Beethoven 26
Brahms 9
Dvorak 2
Mendelssohn 3
Mozart 21
Schubert 12
Schumann 7
Tchaikovsky 14
Wagner 1
a. Does the data listed above comprise a valid probability distribution? Explain.
b. What is the probability that a randomly selected request is for one of the three B's?
c. What is the probability that a randomly selected request is for a Mozart piece?
d. What is the probability that a randomly selected request is not for one of the two S's?
e. Neither Bach nor Wagner wrote any symphonies. What is the probability that a randomly selected request is for a composer who wrote at least one symphony?
f. What is the probability that a randomly selected request is for a composer other than one of the three B's or one of the two S's?