We welcomed a new student into the class.

We discussed Question #2 on Friday’s little quiz. There are actually three different cases: a+c, either a+d or b+c, and b+d. The payoffs are for a+c: A sure loss of $520 (one student chose this as I recall), either a+d or b+c: a 25% chance of gaining $240 and a 75% chance of losing $760. I believe everyone else chose one of these two equivalent bets. The payoff for b+d is a 3/8 chance of $0, a 1/16 chance of gaining $1000, but a 9/16 chance of losing $1000.

Viewed from the point of view of risk, a+c is least risky, but there’s no possibility of a gain. b+d is most risky (and nobody liked it), and the other choices are intermediate in risk.

I then attempted to guess which coin-toss sequences were real and which were fake. I didn’t do very well because quite a few of the ones I guessed were real were really fake! But, at least all the ones I identified as fake were fake. I explained the method I used for guessing. The point of the experiment is that it’s really hard to make up random sequences.

We discussed the Fermi problems. A common method for estimating things (for example, in #1, #2, #3 and #4) was to guess the dimensions of the relevant objects, pretend that they were just a big box and compute volumes or radii as appropriate. Several biology majors in the class gave us informed data about the number of cells in the body. It is quite large (something like 10^{13}, as I recall. Email me if my memory is incorrect on this). Estimating the number of students at UVM and how many books each needs was the method of choice for #5.

We’ll finish this on Friday.

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