using probability concepts and rules, eplain what is wrong with the
statement:
"The probability that a randomly selected car is red is .20, whereas
the probability that a randomly selected car is a red sports car is
.25."

Hi boobee-ga,

Your question is actually quite straight forward once you apply some
set theory to the numbers. First let's consider the common terms:

SET - a group of objects having a similar trait or characteristic

INTERSECTION - given two sets, lets call them A and B, then A
INTERSECTION B produces a group of objects that belong to both A and
B.

UNIVERSE - the set of all objects being considered

A useful tool in seeing how this works in a diagram form is to use
Venn diagrams. An example of one can be found here:
http://whatis.techtarget.com/definition/0,,sid9_gci333063,00.html

You can see that the circles represent sets, the area where two
circles overlap represent an intersection, and the universe is the
rectangle within which all sets are contained. (Don't worry that the
above source uses rectangles as sets..the actual shape isn't critical)

Now that you've got the background information necessary, lets move on
to the question:

The first part of the statement says that 20% of the cars from the
pool being selected are red. This gives us information about a set -
the set of red cars. This could include red sedans, wagons, SUVs, and
sports cars.

Now for the second part of the statement; we need to add another set
to our Venn diagram which depicts the set of sports cars (all colors).
The fact that we don't know the probability here will not matter. So
how can we show this such that all of sports cars are red? Well, we
can draw the sports car set as a circle COMPLETELY CONTAINED WITHIN
the set of red cars.

So what does all this mean? Well, if the probability of selecting a
red car is .20 and all sports cars are red, that means that their
intersection will be .20 - but the statement says that the
probabiility of selecting a red sports car is .25! Obviously this is
impossible, since we are demanding a car that is not only red, but is
also a sports car model!

Note: For the second part of the statment, I could have also said that
the red car set is completely contained within the sports car set (the
opposite), but it would yield the same result since the constraint on
the probability of selecting a red car (.20) limits the intersection
size of this set with ANY OTHER SET to .20

Hope that clears things up...thanks for using Google Answers!

answerguru-ga

Thanks for your answer

This is probably too simple to be the answer you're looking for, but
if only 20% of the cars are red, how can 25% be red sports cars? Even
if all the red cars are sports cars, that's still only 20%.

LOL...even I could answer this one...

Gotta tell you, that was an easy five bucks!