Probability

How to solve probability problems:

Each of the letters in the word
SUPREMACY are on separate cards
face down on the table. If you pick a
card at random, what is the
probability that the letter on it will fall
within the range of "H" and "U" in the
alphabet?

Probability problems are usually about creating ratios, then using them to answer questions related to them.  To find the ratio, find out the total things that can happen. This is the SECOND  or BOTTOM number of the ratio.  Then find the things the problem desires to happen.  This is the FIRST or TOP number of the ratio.  In this way, the desired outcome is set to the total outcomes.  This gives you a fraction.  You can then simplify the fraction and/or convert it to percent or decimal depending on what the problem asks.  The percent triangle can help you with that.

Let's solve the example problem: The problem says there are cards for each letter in the word.  So count them up.  Supremacy has 9 letters.  This is our second or bottom number.  

Then they have defined a range of letters.  Any time a problem defines a PART of the set, they are wanting you to create a FRACTION, which is the ratio of part to whole.  So Figure out which cards are between H and U, including H and U.  We leave out A, C, and E because they are before H and thus out.  We leave out Y because it is after U.  This leaves us with 5 letters.  This is the first or top number.

So our ratio is 5 / 9.

Things to be careful about:  In this set of problems, the word "or" usually means add the probabilities together.  So if they wanted to know the probability of getting an "S" or getting a "U", you would add those probabilities together:  Each is somewhat unlikely though, as getting an "S" has a 1 in 9 chance.  The "or" increases that by 1 in 9.  So 1/9 + 1/9 = 2/9.

Also, please note that this is just ONE event.  If the problem asks for you to draw again, YOU'RE NOT DONE with the math.

The problem would have stated "If you pick a card at random, replace it, and then draw again..." You would multiply the probability of getting the first with the probability of getting the second. So with the "H" to "U", we would have 5/9 * 5/9.  This gives us 25/81.  Note this number is SMALLER, because the chances of it happening GO DOWN.

Other than that, you need to practice these.  Here are some probability games and here are some practice problems.

This description of probability can be displayed in Spanish..