A radio station that plays classical music

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 Does the data listed above comprise a valid probability distribution? Explain.
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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 Does the data listed above comprise a valid probability distribution? Explain. What is the probability that a randomly selected request is for one of the three B’s? What is the probability that a randomly selected request is for a Mozart piece? What is the probability that a randomly selected request is not for one of the two S’s? 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? 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? In each of the following situations, state whether or not the given assignment of probabilities to given outcomes is legitimate, that is, satisfies the rules of a probability distribution. (The assignment of probabilities need not follow common sense understanding of the outcomes!) a. Roll a die and record the count of spots on the up face: P(1) = 0, P(2) = 1/6, P(3) = 1/3, P(4) = 1/3, P(5) = 1/6, P(6) = 0. b. Choose a college student at random and record sex and enrollment status: P(female-fulltime) = 0.56, P(female-part time) = 0.24, P(male-fulltime) = 0.44, P(male- part time) = 0.17 c. Deal a card from a shuffled deck: P(Clubs) = 12/52, P(Diamonds) = 12/52, P(Hearts) = 12/52, P(Spades) = 16/52