# Re: Probability related question and arrays

mensanator@xxxxxxx wrote:
ophidian wrote:
On Mon, 12 Jun 2006 23:32:35 -0700, placid wrote:

Why does everyone have the same chance?

What may be confusing you is the fact that you're choosing items from two
lists, and believe that somehow complicates matters. Let me try to
restate the problem to make it clearer.

Suppose I have a sock drawer containing 8 socks. 7 of the socks are red,
and 1 sock is green. If I blindly reach into the drawer and randomly
choose a sock, I have a 1/8 chance of getting a green sock, and a 7/8
chance of getting a red sock. If there are 7 people behind me, each
blindly choosing a sock after me, we all have the same odds of getting
the green sock.

great example!

It may be worth pointing out again WHY each person has the same
odds. The first person has a strict 1/8 chance of getting the green
sock. But the second person's chance of getting the green sock are
dependent on the the first person getting a red sock, so HIS odds are

7/8 (1st person gets red sock) * 1/7 (only 7 socks remain, one green)

7/8 * 1/7 = 1/8 same as 1st person.

The 3rd person only has a chance if both 1st and 2nd person get
red socks. So his odds are

7/8 * 6/7 * 1/6 = 1/8 same as 1st and 2nd person.

4th person = 7/8 * 6/7 * 5/6 * 1/5 = 1/8
5th person = 7/8 * 6/7 * 5/6 * 4/5 * 1/4 = 1/8
6th person = 7/8 * 6/7 * 5/6 * 4/5 * 3/4 * 1/3 = 1/8
7th person = 7/8 * 6/7 * 5/6 * 4/5 * 3/4 * 2/3 * 1/2 = 1/8
8th person = 7/8 * 6/7 * 5/6 * 4/5 * 3/4 * 2/3 * 1/2 * 1/1 = 1/8

I was getting confused on thus dependancy part of each players chances.

Ok, now this makes sense to me now. Thanks for all the effort everyone.

Now, let's complicate things. Suppose that, in addition to the sock
drawer, I also have a closet with 24 shirts, each a different color. Now
my task is to randomly select 3 shirts and 1 sock. It should be obvious
that the combination of shirts I select can have no impact on my odds of
getting the green sock. How would the closet and the sock drawer
communicate with eachother to let the sock drawer know it has to change
its odds because of the combination of shirts I've chosen? And how could
the sock drawer change its odds, even if it had such information?

Regardless of what happens with the shirt filled closet, my odds of
getting the green sock are 1/8. Regardless of how my additional lists you
introduce into your problem, if you're randomly choosing from the favorite
teams list, your odds of getting a particular team are exactly the same as
those of the other 7 players getting that team.

.