1. Mrs.Volynskaya Alg.2 Ch.1.6 PROBABILITY

2. A probability of an outcome is a number and has two properties:
A probability model has two components: A sample space and an assignment of probabilities.
This is denoted with an S and is a set whose elements are all the possibilities that can occur
Each element of S is called an outcome.
A probability of an outcome is a number and has two properties:
1. The probability assigned to each outcome is nonnegative.
2. The sum of all the probabilities equals 1.

3. S = {1, 2, 3, 4, 5, 6} Let's roll a die once.
This is the sample space---all the possible outcomes
S = {1, 2, 3, 4, 5, 6}
probability an event will occur
What is the probability you will roll an even number?
There are 3 ways to get an even number, rolling a 2, 4 or 6
There are 6 different numbers on the die.

4. The word and in probability means the intersection of two events.
What is the probability that you roll an even number and a number greater than 3?
E = rolling an even number
F = rolling a number greater than 3
How can E occur?
{2, 4, 6}
How can F occur?
{4, 5, 6}
The word or in probability means the union of two events.
What is the probability that you roll an even number or a number greater than 3?

5. P(EF) = P(E) + P(F) - P(EF)
ADDITION RULE
For any two events E and F,
P(EF) = P(E) + P(F) - P(EF)
Let's look at a Venn Diagram to see why this is true:
If we count E E E F F
and then count F,
we've counted the things in both twice so we subtract off the intersection (things in both).

6. ADDITION RULE for Mutually Exclusive Events
If E and F are mutually exclusive events,
P(EF) = P(E) + P(F)
Mutually exclusive means the events are disjoint.
This means E  F = 
Let's look at a Venn Diagram to see why this is true:
You can see that since there are not outcomes in common, we won't be counting anything twice. E F

7. This is read "E complement" and is the set of all elements in the sample space that are not in E
Remembering our second property of probability, "The sum of all the probabilities equals 1" we can determine that:
This is more often used in the form
If we know the probability of rain is 20% or 0.2 then the probability of the complement (no rain) is = 0.8 or 80%