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2. A vehicle travelling in a minor street arrives at an intersection with a main street. The driver has to decide when to cross the (one-way) main street. Suppose that: each vehicle on the main street independently has a 90% chance of being a car and a 10% chance of being a bus, and • the time interval between any two vehicles on the main street has a 50% chance being 4 seconds and a 50% chance being 6 seconds. The driver will cross the main street when x, the time until the next vehicle on the main street to reach the intersection, is at least 3 seconds if that vehicle is a car. If the next vehicle is a bus, the driver will cross if x >= 5 seconds. a. What is the probability that the driver will arrive in a 4-second interval? b. What is the probability that the driver will cross the main street immediately? c. If the driver arrived exactly when a vehicle on the main street has just passed the intersection, what is the probability that he will allow k vehicles on the main street to pass the intersection before crossing? Assume that k is a constant greater than 0.

2. A vehicle travelling in a minor street arrives at an intersection with a main street. The driver has to decide when to cross the (one-way) main street. Suppose that: each vehicle on the main street independently has a 90% chance of being a car and a 10% chance of being a bus, and • the time interval between any two vehicles on the main street has a 50% chance being 4 seconds and a 50% chance being 6 seconds. The driver will cross the main street when x, the time until the next vehicle on the main street to reach the intersection, is at least 3 seconds if that vehicle is a car. If the next vehicle is a bus, the driver will cross if x >= 5 seconds. a. What is the probability that the driver will arrive in a 4-second interval? b. What is the probability that the driver will cross the main street immediately? c. If the driver arrived exactly when a vehicle on the main street has just passed the intersection, what is the probability that he will allow k vehicles on the main street to pass the intersection before crossing? Assume that k is a constant greater than 0.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 39E: The following problem submitted by Daniel Hahn of Blairstown, Iowa, appeared in the Ask Marilyn...
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2. A vehicle travelling in a minor street arrives at an intersection with a main street. The driver has to decide when to cross the (one-way) main street. Suppose that: each vehicle on the main street independently has a 90% chance of being a car and a 10% chance of being a bus, and ● the time interval between any two vehicles on the main street has a 50% chance being 4 seconds and a 50% chance being 6 seconds. The driver will cross the main street when x, the time until the next vehicle on the main street to reach the intersection, is at least 3 seconds if that vehicle is a car. If the next vehicle is a bus, the driver will cross if x>= 5 seconds. a. What is the probability that the driver will arrive in a 4-second interval? b. What is the probability that the driver will cross the main street immediately? C. If the driver arrived exactly when a vehicle on the main street has just passed the intersection, what is the probability that he will allow k vehicles on the main street to pass the intersection before crossing? Assume that k is a constant greater than 0.
Transcribed Image Text:2. A vehicle travelling in a minor street arrives at an intersection with a main street. The driver has to decide when to cross the (one-way) main street. Suppose that: each vehicle on the main street independently has a 90% chance of being a car and a 10% chance of being a bus, and ● the time interval between any two vehicles on the main street has a 50% chance being 4 seconds and a 50% chance being 6 seconds. The driver will cross the main street when x, the time until the next vehicle on the main street to reach the intersection, is at least 3 seconds if that vehicle is a car. If the next vehicle is a bus, the driver will cross if x>= 5 seconds. a. What is the probability that the driver will arrive in a 4-second interval? b. What is the probability that the driver will cross the main street immediately? C. If the driver arrived exactly when a vehicle on the main street has just passed the intersection, what is the probability that he will allow k vehicles on the main street to pass the intersection before crossing? Assume that k is a constant greater than 0.
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