3.1 Introduction to Probability and Technology

Question 1

Probability

Answer 1

Study of randomness, means the chance of an event occurring, basis of statistical inference

Question 2

Randomness

Answer 2

chance behavior is unpredictable in the short run but has a regular and predictable pattern in the long run

Question 3

Law of Large Numbers

Answer 3

as the number of repetitions of an experiment increase, the proportion with which a certain outcome is observed gets closer to the actual classical probability of that outcome, the relative frequency of an event is likely close to the classical probability

Question 4

probability experiment

Answer 4

a repeatable process where the results are uncertain

Question 5

outcome

Answer 5

result of a single trail of a probability experiment

Question 6

sample space

Answer 6

set of all possible outcomes of a probability experiment. usually denoted by S.

Question 7

Event

Answer 7

an outcome or set of outcomes of a probability experiment

Question 8

Probability Model

Answer 8

a mathematical description of a random phenomenon. Has two parts: list of possible outcomes and a way of assigning probabilities to events

Question 9

Axioms of Probability

Answer 9

A probability is a number that is assigned to each member of a collection of events from a random experiment that satisfies the following properties 1. P(S)=1 2. 0<P(E)<1 3. for each two events E1 and E2 with E1nE2=0 P(E1UE2)=P(E1)+P(E2)

Question 10

Approaches to finding probabilities

Answer 10

the classical approach, the relative frequency approach, subjective probability, probability rules for more complicated situations

Question 11

The Classical Approach

Answer 11

uses sample spaces to determine the numerical probability that an event will happen, no experiment, assumes that all outcomes in the sample space are likely to occur. # of outcomes in E/total # of outcomes in the sample space

Question 12

Relative Frequency Approach

Answer 12

uses frequency distributions based on observations to estimate probability. Relies on an actual experiment. Frequency of E/Total number of trails in the experiment=f/n

Question 13

Subjective Probability

Answer 13

the degree to which a given individual believes the event in question will happen

Question 14

The Compliment

Answer 14

the set of outcomes in the sample space that are not included in that event

Question 15

Mutually exclusive

Answer 15

have no outcomes in common, cannot occur at the same time

Question 16

independent

Answer 16

knowing that one occurs does not change the probability that the other occurs

Question 17

Compound Events

Answer 17

Union and Intersection

Question 18

Union

Answer 18

the event consisting of all outcomes that are contained in either of the two events. AUB, A or B

Question 19

Intersection

Answer 19

two events is the event consisting of all outcomes that contained in both of two events A n B, A and B

Question 20

Conditional Probability

Answer 20

quantifies that a second event will occur, given that one has already occurred. P(A l B) A given B