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# Chapter 4 Notes Stats 300

IUPUI

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This 2 page Class Notes was uploaded by Dominique Bohannon on Thursday February 18, 2016. The Class Notes belongs to Stats 300 at Indiana University Purdue University - Indianapolis taught by in Winter 2016. Since its upload, it has received 28 views. For similar materials see Math 104A in Mathematics (M) at Indiana University Purdue University - Indianapolis.

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Date Created: 02/18/16

4.1-4.4 Sample Spaces and Probability 02/11/16 DEFINITIONS: Probability can be defined as the chance of an event occurring. A probability experiment is a chance process that leads to well-defined results called outcomes. An outcome is the result of a single trail of a probability experiment. A sample space is the set of all possible outcomes in a probability experiment. An event consists of outcomes. The complement of an event E, denoted by E with a line on top, is the set of outcomes in the sample space that aren’t included in the outcomes of event. - P(E)= 1-P(EVENT) EXAMPLE: Event: Complement: Rolling a die and getting 4 Getting a 1, 2, 3, 5, or 6 Selecting a letter of the alphabet and getting a vowel Getting a consonant Two events are mutually exclusive events if they cannot occur at the same time - Mutually exclusive = P(A)+P(B) - Not mutually exclusive = P(A)+P(B)-P(A and B) Two events A and B are independent events if the fact that A occurs does not affect the probability of B occurring. - Independent = P(A)*P(B) - Dependent = P(A)*P(BIA) Conditional Probability is the probability that the second event B occurs given that the first event A has occurred. - P(BIA) = P(A and B)/P(A) Different Types of Probabilities: Classical o Deals with Sample Space to determine the numerical probability that an even will happen o # of desired outcomes / total # of possible outcomes Empirical [Relative frequency] o Frequency of desired class / sum of all frequencies Subjective [Educated guess] o Examples being weather forecasting, predicting outcomes of sporting events How to Add o P(A or B) = P(A)+P(B) o P(A or B) = P(A)+P(B)-P(A+B) How to Multiply o P(A and B)= P(A)*P(B) o P(A and B)= P(A)*P(B/A) Counting Rule o Permutation (nPr) n!/(n-r)! o Combination (nCr) n!/(n-r)!r! EXAMPLE OF SAMPLE SPACE Experiment Sample Space Toss a coin Head, Tail Roll a die 1,2,3,4,5,6 Probability Rule 1: - The probability of any event E is a number between and including 0 & 1 Counting Rules (4.4): - The fundamental counting rule is also called the multiplication of choices. - Factorial is the product of all the positive numbers from 1 to a number o n! - Permutation is an arrangement of objects in a specific order. Order matters. o nPr = n! / (n-r)!

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