If people sharing the same birthday raise their hand, how many hands do you expect to see raised? Question: There are 25 people at a party. One person asks everybody to annouycne their birthday, and for anyone who has the same birthday as someone to raise a hand. How many hands do you expect to see raised? For example, if John, Jon, Stephen and Mark all have the same birthday, January 15, but nobody else at the aprty has a matching birthday, the count of hands is four.

RyszardsJh

RyszardsJh

Answered question

2022-11-26

If people sharing the same birthday raise their hand, how many hands do you expect to see raised?
Question: There are 25 people at a party. One person asks everybody to annouycne their birthday, and for anyone who has the same birthday as someone to raise a hand. How many hands do you expect to see raised? For example, if John, Jon, Stephen and Mark all have the same birthday, January 15, but nobody else at the aprty has a matching birthday, the count of hands is four.

Answer & Explanation

Madden Krause

Madden Krause

Beginner2022-11-27Added 12 answers

The probability that a given person raises his hand is the probability that someone else at the party has the same birthday as he does:
1 ( 364 365 ) 24
The expected number of hands raised is
25 25 ( 364 365 ) 24 1.593 ,
by linearity of expectation.

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