X-no-Archive:yes
Well, I don't know if it would matter to the professor that you performed
your own test with a program (per Stan Sieler) or just provide the evidence
from those who did. Those who have taught and tested, now or previously,
might want to advise what the professor should do in such a case. When I
taught, if half the class missed a question, I regarded it as a bad
question, gave credit to those who got it right, but did not penalize those
who got it wrong (I can NOT explain this reasoning in twenty-five words or
less). Technically, b) 1/8 comes closest to the right answer. I hope that
the professor can be reasoned with to see that his answer is wrong, based on
six out of six, and not six out of twenty.

This is just the sort of question that Marilyn vos Savant periodically
answers in Parade magazine (a Sunday newspaper supplement), and might even
be worth sending in to her (she is in the Guinness Book of World Records for
highest IQ, and has parlayed that into a sort of notoriety, and a paycheck
for this column). I remember one of her answers, which enraged some math
professors, to a question involving Let's Make a Deal, in which she answered
that some conditions of what is behind the door you pick and when Monty Hall
asks you if you would like to choose another door, the chances of having
chosen the grand prize was one in two, not one in three. Some mathematicians
wrote that she should stay out of areas that she clearly does not
understand. More than one prof did what others here have done, writing a
program, and to the astonishment of most, got results consistent with vos
Savant's answer.

Unlike balancing my checkbook, this is one kind of problem that I am most
likely to wonder whether I solve it correctly or not, and if I had to bet on
that probability... Bruce already posted correct information where I had it
wrong.

Greg Stigers
http://www.cgiusa.com