Ted writes:

> Wirt writes off three correct answers and pats us on the head,
>  >
>  > Don't ever let anyone tell that probability calculations are easy.

Actually, I did make a mistake in my calculations.

I originally drew the diagram as:

This is where Ted's diagram (slightly modifed) comes in:

 1 - HHHHHH                 1
 2 - THHHHHH                1
 3 - xTHHHHHH               1
 4 - xxTHHHHHH              1
 5 - xxxTHHHHHH             1
 6 - xxxxTHHHHHH            1
 7 - xxxxxTHHHHHH           1
 8 - xxxxxxTHHHHHH          63/64   = 0.9844
 9 - xxxxxxxTHHHHHH         125/128 = 0.9766
10 - xxxxxxxxTHHHHHH        248/256 = 0.9688
11 - xxxxxxxxxTHHHHHH       492/512 = 0.9609
12 - xxxxxxxxxxTHHHHHH           .
13 - xxxxxxxxxxxTHHHHHH          .
14 - xxxxxxxxxxxxTHHHHHH         .
15 - xxxxxxxxxxxxxTHHHHHH        .

but the "weights" are in error. They should have been drawn as the following:

 1 - HHHHHH                 1
 2 - THHHHHH                .5
 3 - xTHHHHHH               .5
 4 - xxTHHHHHH              .5
 5 - xxxTHHHHHH             .5
 6 - xxxxTHHHHHH            .5
 7 - xxxxxTHHHHHH           .5
 8 - xxxxxxTHHHHHH          63/64   = 0.9844 x .5
 9 - xxxxxxxTHHHHHH         125/128 = 0.9766 x .5
10 - xxxxxxxxTHHHHHH        248/256 = 0.9688 x .5
11 - xxxxxxxxxTHHHHHH       492/512 = 0.9609 x .5
12 - xxxxxxxxxxTHHHHHH           .
13 - xxxxxxxxxxxTHHHHHH          .
14 - xxxxxxxxxxxxTHHHHHH         .
15 - xxxxxxxxxxxxxTHHHHHH        .

Without noticing it, beginning on toss 2 and continuing onward, I switched
over to requiring a specific 7-length string (THHHHHHH), while continuing to
call it 6-long. Because of this, I did not properly account for its
probability of occurrence. Only the first string is 6-long (HHHHHHH) and thus
has a probability of 1/64th. All of the others have a probability of only
1/128th, or 0.5 in 1/64th units.

Taking that error into account, the probability of throwing six heads in a
row is recalculated to be approximately 7.8/64ths, or P ~ 0.122. We now all
seem to agree.

My sincere apologies.

However, let me say that the method that I previously outlined (with or
without the simple math errors) is the method that I would advocate if I were
teaching the class as the simplest and most direct way to calculate this
particular answer.

Wirt Atmar