Space Diagrams

Date: 02/28/2002 at 09:12:52
From: Stephen Piggin
Subject: Probability - Space Diagrams.

Hi there,

I am currently studying space diagrams. When there are two or three 
variables I can often succeed, but I have a complex problem that I 
cannot figure out.

A bag contains 3 blue balls, 1 red ball and 1 white ball.
A second bag contains 1 blue ball and 4 red balls.
A ball is chosen at random from each bag.

Draw a sample space diagram to show the possible outcomes.

If you can offer any help it would be appreciated.

Date: 02/28/2002 at 10:35:37
From: Doctor Tim
Subject: Re: Probability - Space Diagrams.

Hi, Stephen.

If I understand what a "space diagram" is, it's analogous to a 
two-dimensional table. I'll try to render one here in computer 
characters:

First Bag: BBBRW

B  B  B  | R  | W 
---------+----+----
Bb Bb Bb | Rb | Wb | b
---------+----+----+
Br Br Br | Rr | Wr | r
Br Br Br | Rr | Wr | r    Second bag: brrrr
Br Br Br | Rr | Wr | r
Br Br Br | Rr | Wr | r
---------+----+----+

So the outcomes are, for example, blue-blue, blue-red, etc. Each of 
the 25 combinations in the diagram is equally likely (since the balls 
are chosen at random from each bag).

Their probabilities are:

  blue-blue = 3/25
  blue-red = 13/25  (12 Br and one Rb, which should be lumped together 
                     if the balls from the different bags look the 
                     same)
  and so forth.

I hope this is what you need!

- Doctor Tim, The Math Forum
  http://mathforum.org/dr.math/   

Date: 03/01/2002 at 03:02:56
From: Stephen Piggin
Subject: Probability - Space Diagrams.

Dear Dr. Tim,

Thank you so much, it seems so easy now, and I am so pleased I 
contacted you.

Thanks again.
Stephen

P.S. My Dad says thanks also!