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Solved: The Birthday the procedure given in Problem,
Chapter 5, Problem 34E(choose chapter or problem)
Problem 34E
The Birthday Problem Using the procedure given in Problem, compute the probability that at least 2 people in a room of 23 people share the same birthday.
Problem
The Birthday Problem Determine the probability that at least 2 people in a room of 10 people share the same birthday, ignoring leap years and assuming each birthday is equally likely, by answering the following questions:
(a) Compute the probability that 10 people have 10 different birthdays.
Hint: The first person’s birthday can occur 365 ways, the second person’s birthday can occur 364 ways, because he or she cannot have the same birthday as the first person, the third person’s birthday can occur 363 ways, because he or she cannot have the same birthday as the first or second person, and so on.
(b) The complement of “10 people have different birthdays” is “at least 2 share a birthday.” Use this information to compute the probability that at least 2 people out of 10 share the same birthday.
Questions & Answers
QUESTION:
Problem 34E
The Birthday Problem Using the procedure given in Problem, compute the probability that at least 2 people in a room of 23 people share the same birthday.
Problem
The Birthday Problem Determine the probability that at least 2 people in a room of 10 people share the same birthday, ignoring leap years and assuming each birthday is equally likely, by answering the following questions:
(a) Compute the probability that 10 people have 10 different birthdays.
Hint: The first person’s birthday can occur 365 ways, the second person’s birthday can occur 364 ways, because he or she cannot have the same birthday as the first person, the third person’s birthday can occur 363 ways, because he or she cannot have the same birthday as the first or second person, and so on.
(b) The complement of “10 people have different birthdays” is “at least 2 share a birthday.” Use this information to compute the probability that at least 2 people out of 10 share the same birthday.
ANSWER:
Solution:
Step 1 of 2:
We have to find the probability that at least 2 people in a room of 23 people share the same birthday.