CASE: Probability That at Least Two People in the Same Room Have the Same Birthday Suppose that there are two people in a room. The probability that they share the same birthday (date, not necessarily year) is 1/365, and the probability that they have different birthdays is 364/365. To illustrate, suppose that you're in a room with one other person and that your birthday is July 1. The probability that the other person does not have the same birthday is 364/365 because there are 364 days in the year that are not July 1. If a third person now enters the room, the probability that that person has a different birthday from the first two people in the room is 363/365. Thus, the (joint) probability that three people in a room having different birthdays is (364/365) (363/365). You can continue this process for any number of people. Find the number of people in a room so that there is about (closest to) a 60% probability that at least two have the same birthday. Hint 1: Calculate the probability that they don't have the same birthday (round your answers to four decimal places)... Hint 2: Excel users can employ the product function to calculate joint probabilities. Solutions: The probability that (the complement event) is people have different birthdays is The probability that at least two people have the same birthday
CASE: Probability That at Least Two People in the Same Room Have the Same Birthday Suppose that there are two people in a room. The probability that they share the same birthday (date, not necessarily year) is 1/365, and the probability that they have different birthdays is 364/365. To illustrate, suppose that you're in a room with one other person and that your birthday is July 1. The probability that the other person does not have the same birthday is 364/365 because there are 364 days in the year that are not July 1. If a third person now enters the room, the probability that that person has a different birthday from the first two people in the room is 363/365. Thus, the (joint) probability that three people in a room having different birthdays is (364/365) (363/365). You can continue this process for any number of people. Find the number of people in a room so that there is about (closest to) a 60% probability that at least two have the same birthday. Hint 1: Calculate the probability that they don't have the same birthday (round your answers to four decimal places)... Hint 2: Excel users can employ the product function to calculate joint probabilities. Solutions: The probability that (the complement event) is people have different birthdays is The probability that at least two people have the same birthday
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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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Transcribed Image Text:CASE: Probability That at Least Two People in the Same Room Have the Same Birthday
Suppose that there are two people in a room. The probability that they share the same birthday (date, not necessarily year) is 1/365, and the
probability that they have different birthdays is 364/365. To illustrate, suppose that you're in a room with one other person and that your birthday is
July 1. The probability that the other person does not have the same birthday is 364/365 because there are 364 days in the year that are not July 1. If
a third person now enters the room, the probability that that person has a different birthday from the first two people in the room is 363/365. Thus,
the (joint) probability that three people in a room having different birthdays is (364/365) (363/365). You can continue this process for any number of
people. Find the number of people in a room so that there is about (closest to) a 60% probability that at least two have the same birthday.
Hint 1: Calculate the probability that they don't have the same birthday (round your answers to four decimal places)..
Hint 2: Excel users can employ the product function to calculate joint probabilities.
Solutions:
The probability that
(the complement event) is
people have different birthdays is
The probability that at least two people have the same birthday
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