I'm no mathemetician but here goes...


"VANCE,JEFF (HP-Cupertino,ex1)" wrote:
>
> Hi all,
>
> (This is way off topic so please delete it now if you are not interested)
>
> My wife just took a biology test where one of the questions was:
>    "What is the probability of tossing 6 heads in a row out of 20 coin
> tosses?"

Hmmm, sounds like they're in the genetics chapter.

> I believe that the number of tosses (20) doesn't matter.

My first thought was to agree with you but then I got my trusty pencil
and paper.

Another way to view this is a bunch of bits randomly set to 0 or 1.

For 6 bits there are 64 possible patterns only 1 of which can be all 1's
(1/64 chance).

If you increase to 7 bits there are 128 patterns, 3 of which can have 6
1's in sequence (3/128 chance, slightly better).

0111111
1111110
1111111

This convinces me that the number of tosses does matter for this
particular situation (note that the probability of 1 coin tossed 100
times coming up heads is still 1/2).

For 20 bits it's 2^19 possible bit patterns.

There are 15 groups of 6 consecutive bits.
Sounds like 15 * 1/64 = 15/64 which is slightly less than 1/4 which
actually sounds reasonable.

But...as we see in the 7 bit case above, it is 3/128 and not 2/128. So
there must be more to this. I'm assuming that having more than 1 string
of 6 1's in the 20 bit pattern is acceptable. If so, your chances
improve above the 15/64. I'm not sure of the actual value. Would require
more thought.


>
> Thanks,
> Jeff