The joint probability distribution of the number X of cars and the number Y of buses per signal cycle at a proposed left-turn lane is displayed in the accompanying joint probability table. p(x, y) 1 2 0.015 0.010 0.025 1 0.030 0.020 0.050 2 0.075 0.050 0.125 3 0.090 0.060 0.150 4 0.060 0.040 0.100 0.030 0.020 0.050 (a) What is the probability that there is exactly one car and exactly one bus during a cycle? (b) What is the probability that there is at most one car and at most one bus during a cycle? (c) What is the probability that there is exactly one car during a cycle? Exactly one bus? P(exactly one car) = P(exactly one bus) = (d) Suppose the left-turn lane is to have a capacity of five cars and one bus is equivalent to three cars. What is the probability of an overflow during a cycle? (e) Are X and Y independent rv's? Explain. O Yes, because p(x, y) = Px(x) • Py(Y). O Yes, because p(x, y) # Px(x) · PylY). O No, because p(x, y) = Px(x) Py(Y). O No, because p(x, y) # Py(x) Py(Y).

The joint probability distribution of the number X of cars and the number Y of buses per signal cycle at a proposed left-turn lane is displayed in the accompanying joint probability table. p(x, y) 1 2 0.015 0.010 0.025 1 0.030 0.020 0.050 2 0.075 0.050 0.125 3 0.090 0.060 0.150 4 0.060 0.040 0.100 0.030 0.020 0.050 (a) What is the probability that there is exactly one car and exactly one bus during a cycle? (b) What is the probability that there is at most one car and at most one bus during a cycle? (c) What is the probability that there is exactly one car during a cycle? Exactly one bus? P(exactly one car) = P(exactly one bus) = (d) Suppose the left-turn lane is to have a capacity of five cars and one bus is equivalent to three cars. What is the probability of an overflow during a cycle? (e) Are X and Y independent rv's? Explain. O Yes, because p(x, y) = Px(x) • Py(Y). O Yes, because p(x, y) # Px(x) · PylY). O No, because p(x, y) = Px(x) Py(Y). O No, because p(x, y) # Py(x) Py(Y).

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section9.3: Binomial Probability

Problem 33E: Sick leave probability that a given worker at Dyno Nutrition Will call in sick on a Monday is 004....

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