Ebf 472 Assignment

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].