1. Definitions Addition Rule Multiplication Rule Tables
Probability
Definitions
Addition Rule
Multiplication Rule
Tables

2. Definition of Probability
Event: Any collection of outcomes of a procedure.
Simple Event: An outcome that is not a collection of simpler components.
Sample Space: All possible simple events.

3. Law of Large Numbers
100,000,000,000,000,000,000,000,000,00 0,0000,000,000
Law of Large Numbers: If an experiment involves many many trials, then the proportion of successes will likely be very close to the theoretical proportion. For example, if you toss a fair coin a billion times, it is highly likely that the proportion of heads will be very close to 0.5.

4. The Addition Rule
P(A OR B) is the probability that either A occurs, B occurs, or both.

5. Rule of Complements
is called the complement of A and represents the outcome of A not occurring.

6. Multiplication Rule
If an experiment is run twice with replacement then:

7. Conditional Probability
The probability of an event A occurring given the knowledge that B has already occurred is denoted by the conditional probability statement:

8. Multiplication Rule
If A and B are independent events then

9. Independence
Two events A and B are independent if one of the three occurs:
P(A and B) = P(A)P(B)
P(A|B) = P(A)
P(B|A) = P(B)
Independence implies knowledge that one occurred does not change the probability that the other will occur.

10. Testing for Independence
Of the 195 students who transferred from the community college last year, 112 took elementary statistics of the transferring students were women and there were 78 women transferring students who took elementary statistics. Are the events “women” and “took elementary statistics” independent for transferring students?

11. Independence Guideline
If the sample size is no more than 5% of the population size, treat the solutions as independent events (even though they are slightly dependent).

12. Tables and Probability
Example: The table below shows the outcome of a recent survey on students’ major.
Science
Humanities
Other
Male 70 60 30
Female 50 80 10
If a student is selected at random find the probability that the student is
Not a science major.
Male given the student is a science major
Female and a humanities major
Male or a humanities major

13. Fundamental Counting Rule
For a sequence of 2 events in which the first can occur in m ways and the second in n ways, the events together can occur in a total of m x n ways.
Example: If you pick a card from a 52 card deck then roll a 6 sided die, there are 52 x 6 = 312 possible outcomes.

14. Combination
The number of ways of selecting r items out of a total of n items to choose from given that the order of the items is not taken into account is
For the TI 83/84, to find the number of ways of selecting 5 items out of a total of 8 items, type in 8 then Math -> PRB -> nCr then 5 then ENTER.

15. The California Lottery
To play the California Lottery, pick 5 numbers from 1 to 56 and one number from 1 to 46. You win $21,000,000 if your numbers are selected.
What is the probability of winning the lottery with one ticket?