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.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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