Planet X has 155 calendar days. What is the probability that in a room with 14 inhabitants of Planet X that at least two of them share a birthday? You may assume that all 155 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 155 birthdays to each of those 14 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 14 inhabitants different birthdays from among the 155 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 155 calendar days. What is the probability that in a room with 14 inhabitants of Planet X that at least two of them share a birthday? You may assume that all 155 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 155 birthdays to each of those 14 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 14 inhabitants different birthdays from among the 155 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 155 calendar days. What is the probability that in a
room with 14 inhabitants of Planet X that at least two of them share
a birthday? You may assume that all 155 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 155 birthdays to each of
those 14 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 14 inhabitants different birthdays from among the
155 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.
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