[at-l] OK..pick a number

[David Hicks" <daveh@usit.net (David Hicks)]

> Hmmm..While this is true as a whole, the original question was what are
> the chances that all the numbers would be below 33.

Right on.  However, I was intending to speak just to Saunterer's proposition
that there is a difference probability of a ticket bought with the numbers
33, 3, 11, 24, 7, and 19 vs. a ticket with the numbers 1, 2, 3, 4, 5, and 6.
Which, BTW, is a different question yet from the

I'm not sure about Pennsylvania's games.  However, in Virginia's games the
order does not matter, and each element is distinct and non-repeatable.  So,
I still hold that no matter how you pick six numbers, once they are picked
they have the same probability of winning as any other six -- based on them
just being another combination or set out of the number of combinations
available, i.e., n!/(r!(n-r)!).  You can randomly generate them, dream them,
use birth dates, etc.  But once they are set, they are all equal.

Which, BTW, is a different question yet from the question of the probability
of any sequentially numbered ticket winning or the question of the winning
numbers all being < "x" number -- which you addressed rather well, IMHO.

> Trail related: What are the chances that out of the first 60 people on the
> trail if you met 6 those 6 would all be in the first 33 people. =)
>

Wow, you were doing great until you got to trying for a trail related
example.  If I were standing on the trail from January on meeting folk, the
first 6 which I meet would be in the first 33 headed north -- which brings
up a major problem with sampling, but let's not go there.

Given what I perceive as the linear progression (physical and temporal) and
self-selection, self-defining, and non-random nature of the trail
experience, I can't think of a good example of truly random experience,
equivalent to a lottery.  Even things such as who will complete, have a life
enhancing/changing hike, be the recipient of great trail magic, experience
certain types of weather, get sick, get hit by lighting, etc. are influenced
by human variables (such a schedule, skill & abilities, stage of life,
personality, demographics, etc.) more than by randomness -- albeit there is
an element of luck.

Chainsaw