perplexus.info :: Probability : Common Birth Dates II

Common Birth Dates II (Posted on 2021-11-17)

Common Birth Dates asked for the expected number of pairs of common birth dates for a cohort of 1000 people whose ages were clustered around a certain value.

Now consider a similar question to the traditional birthday problem: If you attend a concert or other event where people tend to be of a similar age, how large would such an event need to be in terms of number of attendees, so that you'd have at least a 50% probability that there would be at least two people born on the exact same day (year, month and day)?

Again to make things specific: assume the standard deviation about whatever the mean age to be is 12 years and it follows a normal distribution.

Again feel free to vary the assumptions about the distribution.

Submitted by Charlie

Rating: 4.5000 (2 votes)

Solution: (Hide)

clc, clearvars nPeople=147 tot=0; hadTot=0; for trial=1:1000000 hadAny=false; for i=1:nPeople d=round(randn*12*365.25); n(i)=d; end n=sort(n); ct=0; for i=2:nPeople if n(i)==n(i-1) ct=ct+1; hadAny=true; end end tot=tot+ct; hadTot=hadTot+hadAny; end tot/trial hadTot/trial

, where randn is a random number drawn from a normal with mean zero and standard deviation 1, finds that when the number of people is 147, the probability is almost exactly 50% of finding at least one pair of people born on the exact same day.
By the way you'd need about 267 people to have a 90% probability and 378 or 379 to have at least a 99% probability.
If the standard deviation were reduced to 6 years (68% within a 12-year span) you'd need only 104 participants to get at least a 50% probability of at least one pair.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
No Subject	CodyDunning	2023-04-01 02:10:33
Puzzle Answer	K Sengupta	2022-05-11 21:56:15
One more examination	Steven Lord	2021-11-21 14:58:59
explanation of discrepancy	Steven Lord	2021-11-19 10:16:47
analytic attempt	Steven Lord	2021-11-18 07:29:10
No Subject	Steven Lord	2021-11-17 22:25:42

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