SOLUTION: The planet Kepler-166 has an orbital period of 229 days. Consider a group of 20 inhabitants on this planet. What is the probability that at least 2 of them share a birthday?

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Question 918207: The planet Kepler-166 has an orbital period of 229 days. Consider a group of 20
inhabitants on this planet. What is the probability that at least 2 of them share a
birthday?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let be the probability that no two people share a birthday.

If you have 2 people, then the probability the second person has a different birthday than the first person, given 229 possible birthdays, is . For the third person, the probability that the third birthday differs from that of both the first and second is

Following the same line of reasoning, the probability that none of the first twenty people share a birthday is:



Since "at least 2" is the complement of "none", the probability you want is:



You can do your own calculator work.

John

My calculator said it, I believe it, that settles it