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Friday, October 5, 2012

The birthday problem explained

The birthday problem explained

How many people does it take for there to be a 50% chance that a pair in the group has the same birthday? Only 23 people. What about a 99% chance? Maybe even more shocking: 57 people. This is the birthday problem, which every undergrad who's taken a stat course has seen. Steven Strogataz explains the logic and calculations.

Intuitively, how can 23 people be enough? It's because of all the combinations they create, all the opportunities for luck to strike. With 23 people, there are 253 possible pairs of people (see the notes for why), and that turns out to be enough to push the odds of a match above 50 percent.

Incidentally, if you go up to 43 people — the number of individuals who have served as United States president so far — the odds of a match increase to 92 percent. And indeed two of the presidents do have the same birthday: James Polk and Warren Harding were both born on Nov. 2.

The Johnny Carson clip referenced in the article is worth watching. Carson tries to test the results with the audience, but goes about it the wrong way.




Members Only: More on Making Heat Maps in R

You saw how to make basic heat maps a while back, but you might want more flexibility for a specific data set. Once you understand the components of a heat map, the rest is straightforward.

Points per shot on a court




The real A/C repair schedule

ac-repair

My central air conditioner started to suck about a month ago, so I called A/C repair. It took them five appointments, four to assess the problem and one to fix it. The trouble was that for each appointment they'd give me a four-hour window, and every time except the last, they arrived about a half an hour outside the window.

I think they might need to tweak their scheduling system, unless their end game is to set expectations so low that an on-time arrival seems amazing. If that's the case, well, I slow clap in your direction, A/C repair.




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