Intro To Statistics - Chapter 5

Front 1

The collection of all possible outcomes.

Back 1

Sample Space, S

Front 2

Any collection of outcomes from a probability experiement. An event consists of one outcome or more than one outcome.

Back 2

Event, E

Front 3

Events with one outcome.

Back 3

Simple events, ei

Front 4

1.) The probability of any even E, P(E), must be greater than or equal to 0 and less than or equal to 1.

2.) The sum of the probabilites of all the outcomes must equal 1. That is, if the sample space S = {e1,e2,...,en}, then

P(e1)+P(e2)+...+P(en) = 1

Back 4

Rules of Probability

Front 5

This lists the possible outsomes of a probability experiment and each outcome's probability.

Back 5

Probability Model

Front 6

If the probability of the event is 0, it is considered?

Back 6

Impossible

Front 7

If the probability of an event is 1 it is considered?

Back 7

A certainty.

Front 8

An event that has a low probability of occurring. Usually less than 5%

Back 8

Unusual Event

Front 9

The probability of an event E is approximately the number of times event E is observed divided by the number of repetitions of the experiment. P(E) ~~ relative frequency of E = frequency of E / number of trials of experiment

Use this formula when you are given the frequency.

Back 9

Empirical Approach to Approximating Probabilities

Front 10

If an experiment has n equally likely outcomes and if the number of ways that an event E can occur is m, then the proability of E, P(E), is

P(E) = Number of ways that E can occur / number of all possible outcomes = m/n

So, if S is the sample space of this experiment,

P(E) = N(E) / N(S)

Where N(E) is the number of outcomes in E, and N(S) is the number of outcomes in the sample space.

Back 10

Classical Method of Computing Probability

Front 11

A probability obtained on the basis of personal judgement.

Back 11

Subjective Probability

Front 12

Two events are this, if they have no outcomes in common.

Back 12

Disjoint or Mutually Exclusive Events

Front 13

If E and F are disjoint (or mutually exclusive) event, then

P(E or F) = P(E) + P(F)

Back 13

Addition Rule for Disjoint Events

Front 14

For any two events E and F,

P(E or F) = P(E)+P(F)-P(E and F)

Back 14

General Addition Rule

Front 15

If E represents any event and Ec represents the complement of E, then

P(Ec)=1-P(E)

Back 15

Complement Rule

Front 16

If E and F are independent events, then

P(E and F) = P(E)*P(F)

Back 16

Multiplication Rule for Independant Events

Front 17

If events E1, E2, E3, ..., En are independent, then

P(E1 and E2 and E3, and ... and En) = P(E1)*P(E2)*...*P(En)

Back 17

Multiplicatino Rule for n Independent Events