probability

Other Sites:

No luck here yet, there are a lot out there but not many are as user friendly as I prefer. The notes I hvae from this class are pretty sparse so forgive me if I mention something wrong most of this will be from memory.

Basics:

Probability measures or predicts possible favorible outcomes compared with a total number of out comes in a random event.

Probabilities are expressed as numbers between 0 and 1. The closer the number is to 0 the less likely the outcome is. The closer the number is to 1 the more certain the outcome.

The numbers can be expressed in decimal format or as a fraction. When given in decimal it is easy to convert the number over to a percentage.

For example lets say you have a coin and you want to flip it 100 times and count the number of times it lands heads up. When you flip the coin it has 2 possible outcomes, heads or tails. Since you are counting the number of times the heads appears a outcome of 'heads' is considered a favorible outcome. Your total number of outcomes is the number of times you are flipping the coin, or 100 in this case. Lets say that you do this experiment and you obtain a heads 48 times in the 100 flips. This gives a fraction result of 48/100. This is close to 1/2 which is what we would expect the outcome to be. Many times gut intuition can be used to check your work in probability, but be careful, sometimes gut intuition is dead wrong, especially in a probability class.

Sample Spaces:

Permutations:

Order matters for permutations. A permutation is the total number of ways to do something. ORDER MATTERS !!! So if I'm flipping a coin and flip a tales and then a heads, and another time I flip the coin twice more and get heads then tails these two outcomes count as different permutations. (So would heads and heads, and tails and tails).

The total number of permutations is calculated by:

n^r

Where:

n is the number of possible outcomes for each attempt

and

r is the number of attempts.

Example:

Lets say we want to calculate the total number of possible outcomes that we can get from rolling a fair die 3 times. We can figure this out by listing the sample space or by calculating the number of possible permutations. In this case:

n = 6

(you can roll a 1,2,3,4,5, or 6) and

r = 3

(your rolling the die 3 times)

6^3 = 216

Thats a heck of alot better then writing out each possible set of outcomes.

Combinations:

n!