EBF 472 Assignment
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A casino patron will continue
In all questions, you
should use proper notation. Include work and/or an explanation to justify
ALL ANSWERS. That is, don’t just write the final answer, but make sure
you show how and/or why you got it. Correct answers with no work shown
will receive zero credit. All probabilities should be rounded to two
decimal places, unless indicated otherwise. Be neat and organized. If
you’re not, expect an immediate 20% grade reduction. Point values for
each question are in parentheses (out of total possible 100 pts).
ALL QUESTIONS REQUIRE
the use of the Binomial, Geometric, Poisson, or Negative binomial
distributions. CLEARLY STATE WHICH DISTRIBUTION TYPE IS APPROPRIATE, AND
USE IT TO SOLVE. Keep THREE decimal place accuracy in your work.
·
1) Your
instructor used to be a decent basketball player, but he could never shoot free
throws (a “free throw” is a fifteen foot shot attempted without any defenders –
relatively speaking, a free throw is easy to make). On average, your
instructor made just 55% of his free throws in high school. Assume that
your instructor shoots ten free throws.
·
a. What’s
the probability he makes four out of five?
·
b.
What’s the probability that the first free throw he makes is the eighth free
throw that he attempts?
[ Hint you need to use
a different distribution for part b) than for part a)].
·
·
2)
A casino patron will continue making $5 bets on red in roulette until she has
won 4 of these bets. (Prob of winning on “red” = 18/38).
·
a.
What is the probability that she places a total of nine bets?
·
b.
What are her expected winnings when she stops? [Hint: on each bet she either
wins $5 with probability 18/38 or loses $5 with probability 20/38; start with
the expected number of rounds until she wins 4 bets].
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