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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.

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.

A First Course in Probability (10th Edition)
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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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. (c) Calculate the probability that, in a 15 minute period, no sit in customers arrive but at least two takeaway customers arrive at the café.
Transcribed Image Text: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. (c) Calculate the probability that, in a 15 minute period, no sit in customers arrive but at least two takeaway customers arrive at the café.
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