Independent vs. Dependent Events

Date: 06/09/2003 at 16:42:08
From: Sonny
Subject: What is the difference between "independent" and "dependent" 
events?

This is from  the probability of a compound event. Could you give me 
an example?

Date: 06/09/2003 at 16:58:39
From: Doctor Ian
Subject: Re: What is the difference between "independent" and 
"dependent" events?

Hi Sonny,

Two events are independent if the outcome of one has no effect on the
outcome of the other. The classic example would be rolling a pair of
dice. What happens with one die has no effect on what happens with the
other die. 

Two events are dependent if the outcome of one has an effect on the
outcome of the other. The classic example would be drawing cards from
a deck without replacement. The probability of drawing an ace changes
depending on what other cards have already been drawn.  

Probabilities for independent events often involve exponents, while
probabilities for dependent events often involve factorials.  

How many ways are there to roll three dice? There are 6 ways to roll
the first, 6 ways to roll the second, and 6 ways to roll the third, so 
the number of possible outcomes is 

  6*6*6 = 6^3

How many ways are there to draw three cards from a deck without
replacement? There are 52 ways to draw the first one; but now there
are only 51 ways to draw the second (because one card has been
removed); and only 50 ways to draw the third. So the number of 
possible outcomes is 

  52 * 51 * 50 = 52! / (52 - 3)!

Does this help? 

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