Customers arrive at a café according to a Poisson process at the rate of one every three minutes. Each customer can choose to either sit in the café or have a takeaway. The takeaway option is chosen by 39% of customers. Whether a customer chooses to sit in or have a takeaway is assumed to be independent of the choices made by other customers. (a) Calculate the probability that exactly three customers arrive in a 15 minute period. (b) Calculate the probability that, in a 15 minute period, at least two customers who have their order as a takeaway arrive at the café. Calculate the probability that, in a 15 minute period, no sit in customers arrive but at least two takeaway customers arrive at the café. (c)

Customers arrive at a café according to a Poisson process at the rate of one every three minutes. Each customer can choose to either sit in the café or have a takeaway. The takeaway option is chosen by 39% of customers. Whether a customer chooses to sit in or have a takeaway is assumed to be independent of the choices made by other customers. (a) Calculate the probability that exactly three customers arrive in a 15 minute period. (b) Calculate the probability that, in a 15 minute period, at least two customers who have their order as a takeaway arrive at the café. Calculate the probability that, in a 15 minute period, no sit in customers arrive but at least two takeaway customers arrive at the café. (c)

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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