Planet X has 160 calendar days. What is the probability that in a room with 17 inhabitants of Planet X that at least two of them share a birthday? You may assume that all 160 birthdays are equally likely among inhabitants of Planet X. Hint: Instead, find the probability that this does not happen by counting: • How many outcomes are in the sample space? That is, how many ways would there be to assign one of 160 birthdays to each of those 17 inhabitants, where repetition of birthdays is possible? • How many outcomes are in the event of interest (where no two people share a birthday)? That is, how many ways would there be to assign the 17 inhabitants different birthdays from among the 160 birthdays? Use this information to compute a precise probability. Input your answer as a percentage, i.e. a number between O meaning impossible and 100 meaning a certainty. Round your percentage to four decimal places. For example, for 16.6667%, you would input 16.6667.
Planet X has 160 calendar days. What is the probability that in a room with 17 inhabitants of Planet X that at least two of them share a birthday? You may assume that all 160 birthdays are equally likely among inhabitants of Planet X. Hint: Instead, find the probability that this does not happen by counting: • How many outcomes are in the sample space? That is, how many ways would there be to assign one of 160 birthdays to each of those 17 inhabitants, where repetition of birthdays is possible? • How many outcomes are in the event of interest (where no two people share a birthday)? That is, how many ways would there be to assign the 17 inhabitants different birthdays from among the 160 birthdays? Use this information to compute a precise probability. Input your answer as a percentage, i.e. a number between O meaning impossible and 100 meaning a certainty. Round your percentage to four decimal places. For example, for 16.6667%, you would input 16.6667.
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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Transcribed Image Text:Planet X has 160 calendar days. What is the probability that in a room with 17 inhabitants of
Planet X that at least two of them share a birthday? You may assume that all 160 birthdays are
equally likely among inhabitants of Planet X.
Hint: Instead, find the probability that this does not happen by counting:
• How many outcomes are in the sample space? That is, how many ways would there be to
assign one of 160 birthdays to each of those 17 inhabitants, where repetition of birthdays is
possible?
• How many outcomes are in the event of interest (where no two people share a birthday)?
That is, how many ways would there be to assign the 17 inhabitants different birthdays from
among the 160 birthdays?
Use this information to compute a precise probability.
Input your answer as a percentage, i.e. a number between O meaning impossible and 100
meaning a certainty. Round your percentage to four decimal places. For example, for
1/6
≈ 16.6667%, you would input 16.6667.
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