As part of a recent Radiolab episode on randomness, the hosts visit Statistics Professor Deborah Nolan at the University of California, Berkeley. She has the class do an exercise: while she is out of the room, two groups each generate a list of one hundred coin flips. One group flips a penny and records the results as a series of H's and T's, the other group imagines they are flipping a coin and writes what they suppose the results would be.
The two lists are then written on the chalkboard. The professor returns, takes a look at the two lists, and promptly identifies which list is the result of actual coin flips and which one was faked.
How did she do it?
4 comments:
My guess:
She chose the series with the longest sequence of consecutive Hs or Ts as the random one.
You didn't listen to the show, did you?
No....
Does that mean that I'm right, or that I'm laughably wrong?
My reasoning was simple: people tend to think that long runs of [T|H] are somehow "not random", so people "mentally" flipping a coin will tend more towards strict alternation. A hundred trials is a pretty small sample, but I'd expect to see a run of at least 4 or 5 in there. QED.
You were perfectly right. The coin-flippers had a run of seven tails. The fakers had runs of at most four.
A calculator named Soren gave a figure for the probability of a run of seven identical tosses in a set of 100. Deriving this number might be a more suitable challenge for your skills.
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