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Assume you have a gathering of 2,000 people. a) Can you assure 100 % that at...

Assume you have a gathering of 2,000 people. a) Can you assure 100 % that at least two people will celebrate their birthday on the same day of any given month? b) would it make any difference if the year you are considering is a leap year?

Math   Statistics-And-Probability   
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Answer #1

Number of people= 2000

P( atleast two people will celebrate their birthday on the same day of any month b) = 1- P ( all the people have their birthday on different days in all months b)

= 1-0 = 1 because maximum number of unique birthdays can be 365 ( one birthday per day of year )

Hence we are 100% sure

2.) In leap year, number of days are 366, therefore maximum number of unique birthdays can be 366, so all 2000 people cannot have unique birthdays, hence probability in 1 will remain unchanged

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