13 thoughts on “The Birthday Puzzle”

  1. I already knew the answer because it’s my favorite number. 🙂 Also, my first year in college, 5 people on 2 floors of our wing of the dorm (about 60-70 people) had the same birthday, too. Same year, even.

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  2. How many people would you think would have to be in a room that your odds would be almost sure that they would have exactly the same birthday on the same day?”
    Ed guesses 1,000, which suggests he doesn’t understand the question, since 366 people already ensure a match.
    I think Ed understood Johnny’s question perfectly fine, and the “math expert” here misses is reasonable interpretation. If your birthday is today (October 2), having 366 people in the room doesn’t “ensure” a match. There will be lots of empty days, and lots of doubling up.
    Johnny may have screwed up the question, but if Ed interpreted it to mean, “How many random people do I need to have in a room to guarantee with a 99% likelihood that at least one of them is born on October 2 so shares a birthday with YOU,” then 1,000 seems like a pretty good off-the-cuff guess.

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  4. I know this problem well (and Kahn has a nice video explanation of the problem, if you don’t want to follow the NY times text). It is an important mathematical concept, that comes up in many different contexts.
    I love that the author has a loop closure with the Johnny Carson video (though I hadn’t heard about it before).
    I agree with Ragtime that Carson mis-worded the problem (garbled it so that you can’t tell exactly what he’s asking). The precision matters. And, that there were wrong follow-up experiments done (oh, and I hadn’t ever worked out the problem for even odds that someone shares *your* birthday, and am surprised that it’s only 253).
    (The article is great, even for me, who knows the b-day problem well. I’ve always wondered if seasonal variations in birth rate made a difference — they don’t)

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  6. Weirdly, I’ve been thinking about this because an ex-boyfriend and a close friend share a birthday – and it’s today! (And one of them is hitting a big milestone this year.) What are the odds of that?

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  7. The odds that two specific people share a birthday and that day is today should be the same as the odds of three people sharing a birthday, or 1/(365*365), which is a 1 in 133,225 chance.
    Of course, unlike your birthday, “today” changes everyday, so if you think about the birthday problem every day, eventually the odds come down to just 1 in 365.
    And if you open up the group of people who might share a birthday, and you know a fairly broad group of people of about 1,000 people or more, it will always be true that you know two people with the same birthday, and that birthday is today. In fact, every time I log on to Facebook, I am told whose birthday it is today, and it is frequently two people’s birthdays, and it is always today.

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  8. Hey, my birthday is actually really close to being today :-).
    I believe that the odds that three people share today as their birthday is 1/365^3 (and that day is today) not 1/365^2 (like whether 3 365 sided die will come up on the same coin v 2).
    Now, the odds that two people would share a birthday, that it would be today, and that day should be the day that the NY times chose to write an article on the birthday problem & that Laura chose to post on it is probably incalculable, but we could make a stab at it, by multiply by the odds that the NY times would write on the b-day party problem and the odds that when that happen, Laura would link to it).

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  9. When I asked, “What are the odds of that?” I was being rhetorical, but I see it is indeed possible to figure out the odds. Now my head hurts.

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  10. This is just up my alley- it sounds like an SAT math question. Much fun!
    And I’ve got a rare situation in terms of birthdays. The person who shares mine… us my son!

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  12. So, in this sample, we have 3 commenters who share a bday with someone they know. Of course, the conditional probability that we bday sharers will post is high. I wonder if we can estimate the size of the commentor pool, if we assume a 96% probability that someone who shares a bday will post.
    (we are doing the problem now, unlike Carsons experiments.)
    BTW Ragtime is right, except 1/365^3. I misstated the problem as 3 people and today, which would be 1/365^4.

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