 Dependent: — Occurrence of one affects the probability of the other

 Independent: — Occurrence of one does not influence the probability of occurrence of the other

Example –

Independent Events

E1 = heads on one flip of fair coin

E2 = heads on second flip of same coin

Result of second flip does not depend on the result of the first flip.

Dependent Events

E1 = rain forecasted on the news

E2 = take umbrella to work

Probability of the second event is affected by the occurrence of the first event

What about drawing a King from a deck of 52 cards?

The probability is 4 out of 52, right?

If you returned the card you chose to the deck,

your second draw would be *independent* of the first draw.

Ok. Sounds good.

Now, suppose you *didn’t* return that card back into the deck. What is the probability of drawing a King?

Let’s see…. 4 out of 51.

By not returning the first card into the deck, the probability of drawing a King has increased, (assuming the first card wasn’t a King). In doing so, the outcome of the second draw is *dependent* on the first draw.

http://www.cliffsnotes.com/WileyCDA/CliffsReviewTopic/Dependent-Events.topicArticleId-25951,articleId-25912.html

One more short example:

What is the possibility of flipping the same coin twice and having it come up heads? Well, the second flip of the coin is *dependent* on the outcome of having heads on the first try.

Probability of two heads in a row is:

1/2 * 1/2 = 1/4

Here’s a few websites that explains dependent and independent events a little more indepth:

http://www.learningwave.com/chapters/probability/dependent_independent.html

http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=325

http://www.saskschools.ca/curr_content/mathb30/prob/les6/notes1.htm

Good luck in your studies,

~ Mitch ~