business stats

A value between 0 and 1 inclusive that represents the likelihood a particular event happens

Probability

A process that leads to the occurrence of one and only one of several possible results

Experiment

A particular result of an experiment

Outcome

A collection of one or more outcomes of an experiment

Event

…is based on the assumption that the outcomes of an experiment are equally likely

-rolled a die or flipped a coin

Classical probability

to find Probability of an Event you would do…

number of favorable outcomes/ number of all possible outcomes

There are three formulas to help determine the number of outcomes in probability…

Multiplication
Permutation
Combination

Any arrangement of r objects selected from a single group of n possible objects

Permutation

If the order of the selected objects is not important, any arrangement is called a

combination

The number of combinations is less than the number of

permutations

An event of outcomes when the order of the outcomes does not matter

Combination

…. is the second type of probability

Empirical probability

It is based on observation, counting and recording experimental outcomes

-what actually happened in the real world, you don't need to calculate "how many ways" something could happen—you just count how many times it did happen.

Empirical probability

The probability of an event based on a collection of observations or data

Empirical Probability

An empirical probability is based on…

relative frequencies

The empirical approach is based on the…

law of large numbers

Over a large number of trials, the empirical probability of an event will approach its true probability

Law of Large Numbers

If there is little or no experience on which to base a probability, it is estimated…

subjectively

The likelihood (probability) of a particular event happening that is assigned by an individual based on whatever information is available

Subjective Concept of Probability

Two events are mutually exclusive if they cannot occur at the same time

Mutually Exclusive

A set of events is collectively exhaustive if together they include all possible outcomes of the experiment

Collectively Exhaustive

If events are mutually exclusive, the special rule of addition is

P(A or B)=P(A) + P(B)

If the set of events is mutually exclusive and collectively exhaustive, their probabilities add up to …

1

… is used to determine the probability of an event happening by subtracting the probability of an event not happening from 1

The complement rule

A probability that measures the likelihood two or more events will happen concurrently

Joint Probability

The occurrence of one event has no effect on the probability of the occurrence of another event

Independence

If two events are not independent, they are…

dependent

The probability of a particular event, given that another event has occurred

Conditional Probability

… A table used to classify sample observations according to two or more identifiable categories or classes.

Contingency Table

-A visual that is helpful in organizing and calculating probabilities for problems with several stages

-Each stage of the problem is represented by a branch of the tree

-Label the branches with the probabilities.

tree diagram

chapter 6 discrete probability distributions

chapter 6 discrete probability distributions

A listing of all the outcomes of an experiment and the probability associated with each outcome

Probability Distribution

1. The probability of a particular outcome is between 0 and 1 inclusive

2. The outcomes are mutually exclusive

3. The list of outcomes is exhaustive. So the sum of the probabilities of the outcomes is equal to 1.

What is a Probability Distribution?

In any experiment of chance, the outcomes occur randomly and are called…

random variables

A variable measured or observed as the result of an experiment

Random Variable

A random variable that can assume only certain clearly separated values

Discrete Random Variable

…are usually the result of counting

Discrete variables

The data are summarized with a…

relative frequency table

A random variable that may assume an infinite number of values within a given range

Continuous Random Variable

There are four requirements of a binomial probability distribution

There are only two outcomes (success or failure) that are mutually exclusive
The number of trials is fixed and known
The probability of a success is the same for each trial
Each trial is independent of any other trial

Poisson describes the number of times some event occurs during a

specified interval

The interval can be…

time, distance, area or volume

Binomial counts … out of fixed attempts

successes

Poisson counts … that occur randomly over time or space

events

he Poisson distribution closely approximates the Binomial when the number of trials is … and the probability of success is …

large and small

The curve approaches but never touches the x-axis

Asymptotic

he signed distance between a selected value, designated x, and the mean, divided by the standard deviation,

z value