Practical Management Science
5th Edition
ISBN: 9781305734845
Author: WINSTON
Publisher: Cengage
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Chapter 10, Problem 38P
It is surprising (but true) that if 23 people are in the same room, there is about a 50% chance that at least two people will have the same birthday. Suppose you want to estimate the probability that if 30 people are in the same room, at least two of them will have the same birthday. You can proceed as follows.
- a. Generate random birthdays for 30 different people. Ignoring the possibility of a leap year, each person has a 1/365 chance of having a given birthday (label the days of the year 1 to 365). You can use the RANDBETWEEN function to generate birthdays.
- b. Once you have generated 30 people’s birthdays, how can you tell whether at least two people have the same birthday? One way is to use Excel’s RANK function. (You can learn how to use this function in Excel’s online help.) This function returns the rank of a number relative to a given group of numbers. In the case of a tie, two numbers are given the same rank. For example, if the set of numbers is 4, 3, 2, 5, the RANK function returns 2, 3, 4, 1. (By default, RANK gives 1 to the largest number.) If the set of numbers is 4, 3, 2, 4, the RANK function returns 1, 3, 4, 1.
- c. After using the RANK function, you should be able to determine whether at least two of the 30 people have the same birthday. What is the (estimated) probability that this occurs?
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2.16
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27
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5
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90%
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Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)
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Chapter 10 Solutions
Practical Management Science
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