Thursday, June 25, 2009

Stochasticity

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?

Wednesday, June 17, 2009

Combinatorics for fun and profit

Score in my office:

This problem - 3
Hackers - 0

Suppose Steve and Rasalom are evenly matched at playing Azad. That is, any time Steve and Rasalom play Azad, each has a 50% chance of winning (there are no draws). Which scenario is more likely: a) Steve and Rasalom play 4 times and Steve wins exactly 3, or b) Steve and Rasalom play 8 times and Steve wins exactly 5.

Justify your answer; right guesses will be ignored, wrong guesses will be mocked.