# Re: Probability related question and arrays

*From*: "placid" <Bulkan@xxxxxxxxx>*Date*: 13 Jun 2006 16:50:44 -0700

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.

.

**References**:**Probability related question and arrays***From:*placid

**Re: Probability related question and arrays***From:*ophidian

**Re: Probability related question and arrays***From:*placid

**Re: Probability related question and arrays***From:*mensanator@xxxxxxx

**Re: Probability related question and arrays***From:*placid

**Re: Probability related question and arrays***From:*ophidian

**Re: Probability related question and arrays***From:*placid

**Re: Probability related question and arrays***From:*ophidian

**Re: Probability related question and arrays***From:*mensanator@xxxxxxx

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