Probability Continued,,, Nonuniform Sample Space

This posting was saved as a draft back from our original probability discussion at the beginning of July and unfortunately did not appear "officially" until now. What are the odds of that happening?! Well, in this case they were pretty likely. So, this is a continuation of our probability discussion. Remembering back we worked with the likelihood that an event would happen equally (uniform sample space). Our example was what our odds were of getting a 6 on a regular die. Today we are going to continue learning about probability- and we are going to find out how to determine the odds of an event happening.

An example of a nonuniform event would be to pick a day of the week using only the first letter of that day (ex. M=Monday, T=Tuesday, S=Saturday, etc.). This becomes trickier since "T" can also stand for Thursday and "S" can also stand for Sunday. This means that "T" or "S" is twice as likely to happen than M, W, F.  We can look into this further by imagining we have a bag with 5 red balls, 2 green balls, and 3 blue balls. What are our following probabilities?
a) Red?     b)Blue?
b) A primary color?

What do we know? Well, we know we have a total of 10 balls. To solve the first question we need to realize- of those 10 balls 5 are red. So, our odds would be 5 out of 10 which we can then reduce down to 1 out of 2. We would draw a red ball 50% of the time. What about blue? There are 3 blue balls out of 10. We can't reduce this down so 3 divided by 10 is .30 which would mean we were drawing a blue ball 30% of the time. What about our last question, if we drew a primary color- red, yellow, or blue. We would have 8 balls that were primary colors and 2 that were green (secondary color). So 8 divided by 10 would make it so we drew balls that were primary colors 80% of the time.

A formula for figuring out Nonuniform Sample Space is as follows:

P(A)=              Measure of the outcomes associated with the event A
                        Measure of all outcomes in the sample space S

To associate this with our last problem we would say:

The Probability of drawing only primary colors is:  8 primary colors
                                                                   10 total colors

So we have 8 over 10 which is equal to .80 or 80% (we can reduce down to 4 over 5 to also get .80)

Included here is a link to a webpage that discusses the odds of an event happening and also the odds of it not happening. It also gives formulas used and great tips.
http://www.mathgoodies.com/lessons/vol6/intro_probability.html

Additionally, we can extend the idea of pulling more balls out of the bag and probability continued- with the following video: