Problem 4 Study the special case of the "small world" problem called the "birthday problem" (http://en.wikipedia.org/wiki/Birthday_problem). Disregarding the possibility of a February 29 birthday, suppose a randomly selected individual is equally likely to have been born on any one of 365 days. a. If eight people are randomly selected, what is the probability that all have different birthdays? b. If eight people are randomly selected, what is the probability that at least two have the same birthday? c. Create a table for k people being randomly selected, from k = 2 to k = the smallest value for which there is at least a 50-50 chance that at least two people will have the same birthday. (you should use Excel)

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Problem 4
Study the special case of the "small world" problem called the "birthday problem"
(http://en.wikipedia.org/wiki/Birthday_problem). Disregarding the possibility of a February 29
birthday, suppose a randomly selected individual is equally likely to have been born on any one
of 365 days.
a. If eight people are randomly selected, what is the probability that all have different
birthdays?
b.
If eight people are randomly selected, what is the probability that at least two have the
same birthday?
c.
Create a table for k people being randomly selected, from k = 2 to k = the smallest value
for which there is at least a 50-50 chance that at least two people will have the same
birthday. (you should use Excel)
Transcribed Image Text:Problem 4 Study the special case of the "small world" problem called the "birthday problem" (http://en.wikipedia.org/wiki/Birthday_problem). Disregarding the possibility of a February 29 birthday, suppose a randomly selected individual is equally likely to have been born on any one of 365 days. a. If eight people are randomly selected, what is the probability that all have different birthdays? b. If eight people are randomly selected, what is the probability that at least two have the same birthday? c. Create a table for k people being randomly selected, from k = 2 to k = the smallest value for which there is at least a 50-50 chance that at least two people will have the same birthday. (you should use Excel)
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