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kolombo
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Posts: 5
Joined: March 21st, 2010, 2:04 am

generalizing the birthday problem

October 12th, 2010, 9:22 pm

for the birthday problem, the probability that at least 2 people out of N total share the same birthday is 1-365*364*....*(365-N+1)/365^Nwhat would be the probability that at least k people out of N total (k<N) share the same birthday (any date)?what about the probability that at least k people out of N total (k<N) share a specified birthday (a pre-determined fixed date)?
 
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alexrem
Posts: 12
Joined: April 3rd, 2009, 4:57 pm

generalizing the birthday problem

October 13th, 2010, 2:14 am

For the first one use inclusion-exclusion principle; for the second just do 1 - P(nobody is born on specified date) - P(1 person bought that date)-...-P(k-1 people born on that date), each of the terms is easy to calculate.I am not sure if the answers simplify.
 
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list
Posts: 2041
Joined: October 26th, 2005, 2:08 pm

generalizing the birthday problem

October 13th, 2010, 10:24 am

QuoteOriginally posted by: kolombofor the birthday problem, the probability that at least 2 people out of N total share the same birthday is 1-365*364*....*(365-N+1)/365^Nwhat would be the probability that at least k people out of N total (k<N) share the same birthday (any date)?what about the probability that at least k people out of N total (k<N) share a specified birthday (a pre-determined fixed date)?there exists other approach for k = 2 to construct a solution. The number of favourable events is a permutation of N taking k at a time. The total number of outcomes are 365^N
 
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list
Posts: 2041
Joined: October 26th, 2005, 2:08 pm

generalizing the birthday problem

October 13th, 2010, 2:16 pm

QuoteOriginally posted by: listQuoteOriginally posted by: kolombofor the birthday problem, the probability that at least 2 people out of N total share the same birthday is 1-365*364*....*(365-N+1)/365^Nwhat would be the probability that at least k people out of N total (k<N) share the same birthday (any date)?what about the probability that at least k people out of N total (k<N) share a specified birthday (a pre-determined fixed date)?there exists other approach for k = 2 to construct a solution. The number of favourable events is a permutation of N taking k at a time. The total number of outcomes are 365^NSorry, i lost the factor 365 in the numerator.
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