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Problem 2-26 - Northside Rifle Team

Problem 2-26 - Northside Rifle Team. Jan White BUS 340 October 31, 2006 Slide #1. Dick and Sally are markspersons on the Northside Rifle Team – their statistics are:. Dick hits the bull’s-eye 90% of the time Sally hits the bull’s-eye 95% of the time Jan White BUS340 Slide #2.

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Problem 2-26 - Northside Rifle Team

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  1. Problem 2-26 - Northside Rifle Team Jan White BUS 340 October 31, 2006 Slide #1

  2. Dick and Sally are markspersons on the Northside Rifle Team – their statistics are: • Dick hits the bull’s-eye 90% of the time • Sally hits the bull’s-eye 95% of the time • Jan White • BUS340 • Slide #2

  3. Part A.What is the probability that either Dick or Sally or both will hit the bull’s-eye if each takes one shot? • Dick = Event A, Sally = Event B • P(A) + P(B) - P(A and B) = P(A or B) • Not mutually exclusive (there are other outcomes) • .9 + .95 - .855 = .995, or 99.5% of the time either Dick or Sally or both will hit the bull’s-eye. • Can also be shown in terms of “misses”, as 1 – {P(NA) x P(NB)} = 1 – (.1 x .05) = 1 - .005 = .995, or 99.5% chance of not missing • Jan White • BUS340 • Slide #3

  4. Part B. What is the probability that Dick and Sally will both hit the bull’s-eye? • P(A) x P(B) = .9 x .95 = .855, or 85.5% of the time Dick and Sally will both hit the bull’s-eye • Joint probability of multiple, independent events occurring at the same time. • Jan White • BUS 340 • Slide #4

  5. Part C. Did I have any assumptions in answering the questions in parts A and B? If so, do I think I was justified? • Yes, I had the assumption that the events were completely independent. • My justification is that Dick’s marksmanship would not affect Sally’s, and vice-versa, as they each had a record of performance. • Jan White • BUS 340 • Slide #5

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