It has been noted that Roger Ebert and Paul McCartney were born on the same day (year, month and day). How many such coincidences should you expect?
To make things specific, assume there are 1000 celebrities of such stature and recency, and that whatever their average age is, the standard deviation of their ages is 12 years and follows a normal distribution. Of course the date is rounded to the day; don't worry about the hours.
Feel free to vary the assumptions for bonus answers.
I don't see any reason to expect that the ages are normally distributed. Assume, instead, that the ages are uniformly distributed over 50 years (between age 20 and 70). There are 18,262 days in this age range. And the number of pairs of celebrities are 1000*999/2 = 499,500. The expected number of pairs born on the same day = 499,500/18,262 = 27.35, which is surprisingly close to Jer's rough estimate of 25.7.
Jer's solution is excellent, since it deals with the normal probability distribution which I wanted to avoid. However, Jer's approach includes an implicit underestimate of the number of pairs of celebrities, by assuming that all days have 3 celebrities born on each day, which is 3*2/2 = 3 pairs per day. If one day has only 2 celebrities born on that day and another has 4, then there are 7 pairs of celebrities sharing a birthday on one of those two days, not 6 pairs. My approach avoids this problem. The only reason that our estimates are so close is that 1000/365 is only 2.74 per day, and by rounding up to 3 days Jer inadvertently compensates for the other problem. If we had assumed 1200 celebrities instead of 1000, then Jer's approach would have rounded down to 3 celebrities per birthday, and the rough errors would have reinforced each other, not offset each other. My approach actually avoids both problems.
Another rough estimate
