Chapter 6 - Probability Math 22 Introductory Statistics

Simulating Repeated Coin Tosses  Simulation with the TI – 83  Empirical Probability (Observed Probability) – The probability of a specific event as it was observed in an experiment.  Theoretical Probability – The true probability of a specific event of interest. Often an unknown value estimated by an empirical probability.

Probability  Probability - A numerical value that is associated with some outcome and indicates how likely it is that the outcome will occur.  Experiment - The process of making an observation or taking a measurement.  Sample Space (S) - Listing of all possible outcome of an experiment.  Event - Subset of the sample space.

Probability of an Event The probability of an event A is the sum of the outcomes in A. We write it as P(A). P(event) = # of times that the event can occur total # of outcomes in the experiment

Assigning Probabilities to Individual Outcomes In assigning probabilities to the individual outcomes in a sample space, two conditions must be satisfied:  The probability of each outcome must be between 0 and 1, inclusive.  The probabilities of all outcomes in the sample space must sum to 1.

Calculating the Probability of an Event  Define the experiment and list the outcomes in the sample space.  Assign probabilities to the outcomes such that each is between 0 and 1.  List the outcomes of the event of concern.  Sum the probabilities of the outcomes that are in the event of concern.

Law of Large Numbers  As the number of times an experiment is repeated increases (as n gets larger), the value of the empirical probability will approach the value of the theoretical probability.

Odds and Compliment of an Event  Odds  Compliment of an Event – The probability of that event not happening.

Mutually Exclusive and Independent Events  Mutually Exclusive Events - when 2 events cannot happen at the same time  Independent Events - When one event does not affect the outcome (or the probability) of the other event.

General Addition Rule  Let A and B be events then,

Conditional Probability  Conditional Probability - The probability of an event occurring given that another event has already occurred.

The Multiplication Law for Independent Events  Let A and B be two independent events then P(A and B)=P(A)P(B)