Patterico's Pontifications

4/18/2009

An Analogy

Filed under: — Patterico @ 4:17 pm

By analogy, the birthday problem posits that you have a 1 in 365 chance of having the same birthday as a randomly picked person — but in a room of 122 people, that you will match someone go up to around 1 in 3. So, let’s say that there is a famous roomful of 122 people called the “murder room” — so named because all 122 people have murder convictions. We go into that room to see if someone matches your birthday, and someone (call him “Ralph”) turns out to be a match to you. Now assume further that Ralph is charged with murder because of this coincidental match (an unlikely hypothetical, but run with it for now).

Now, say that Ralph’s attorney wants to hide from the jury the fact that Ralph was picked from a room of 122 people, because she suspects that the jury will (correctly) conclude that the room in question is the infamous murder room. So, instead, the jury is not told how we found Ralph — and this fact is hidden to protect Ralph’s rights. Now, if a jury is not told that Ralph was picked from a room of 122 people, how in the world are you going to give them a 1 in 3 number and have it make any sense? The only rational thing you can tell them is that 1 in 365 people share the same birthday — a number that tells the jury that there are millions of people in the world like Ralph.

If Ralph’s attorney wants to tell the jury that Ralph was plucked from a room with 122 people, then it makes sense to explain to the jury that, before we knew that Ralph was in the room, we could assume that there was a 1 in 3 chance that someone in the room would match your birthday. But without that fact, the 1 in 3 number is worse than meaningless.

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