Jeff Vance writes:

>This has been interesting reading.  I now have the test in front
>of me along with the answer deemed correct by the professor.
>
>I repeat it here verbatim:
>
>   'The probability for six straight "heads" on 20 independent coin
>    tosses is:
>      a) 1/4
>      b) 1/8
>      c) 1/16
>      d) 1/32
>      e) 1/64 '
>
>And the correct answer is supposed to be 1/64.
>Should my wife send some of the other solutions to this
>professor?

Yes. The professor either asked the wrong question or has the wrong
answer. 1/64 is the probability of getting six heads in six coin tosses.
That's not what he asked.

-- Bruce

PS. On eight occasions in the last nine years, I've been asked by friends
who were expecting babies to predict the sex. In six of the eight cases,
I issued a prediction, and in two cases, I said I couldn't tell. All six
of the predictions were correct. How likely is it that my success is due
to pure chance? That is, how does a refusal to provide a data point in
two cases affect the probability calculation?

- B

PPS. This isn't as off-topic is it seems. Being able to analyze the
results of a predictive test is important to validating algorithms. In
fact, last night after reading about Gavin's 26,000,000 coin tosses, I
spent a fair amount of time in Knuth V.2 reading about how to evaluate
random number generators. That's important, since Gavin didn't actually
toss a coin 26,000,000 times; he just ran a linear congruential generator
26,000,000 times. The validity of Gavin's simulation depends on the
behavior of the algorithm.

I'm way too pushed at the moment to program any of these tests, but Gavin
might want to take a stab :-).

- B


--------------------------------------------------------------------------
Bruce Toback    Tel: (602) 996-8601| My candle burns at both ends;
OPT, Inc.            (800) 858-4507| It will not last the night;
11801 N. Tatum Blvd. Ste. 142      | But ah, my foes, and oh, my friends -
Phoenix AZ 85028                   | It gives a lovely light.
btoback AT optc.com                |     -- Edna St. Vincent Millay
Mail sent to [log in to unmask] will be inspected for a
fee of US$250. Mailing to said address constitutes agreement to
pay, including collection costs.