Probabilit

3 Methods of Assigning probability

1. Classical Probability Assessment. 2. Relative Frequency Assessment 3. Subjective Probability Assessment.

Experiment

A process that produces a single outcome, whose result cannot be predicted with certainty.

Event

An event is a specified subset of a sample space. A specific possible outcome of an experiment. Events are often further denoted with a letter Such as 'Event A'.

Probability

In an experiment where there is a finite number of possible outcomes, the probability of an event occurring is the Proportion of possible outcomes in the sample space which result in the event of interest occurring. The value of probability must always lie between 0 and 1, impossible being 0 and certain being 1. May be expressed as a percentage, fraction or proportion.

Multiplication Rule for Dependent and or Conditional Events

P(A and B) = P(A) * P(B | A)

P(A and B) =

P(A ∩ B)

Conditional Probability for any two Events:

P(E1 | E2) = P(E1 and E2) / P(e2)

Conditional Probability for independent Events

P(E1 | E2) = P(E1)

Pr(A or B) =

Pr (A ∪ B)

Addition Law for Mutually Exclusive Events

Pr(A ∪ B) = Pr(A) + Pr(B)

Addition Law for Independent Events

Pr(A ∪ B) = Pr(A) + Pr(B) - Pr(A∩ B)

Multiplication Law For Independent Events

Pr(A∩ B) = Pr(A) × Pr(B)

Relative Frequency probability Assessment step by step process.

Step 1: Define the experiment Step 2: Define the event of interest Step 3: Determine the TOTAL number of occurrences Step 4: for the event of interest, determine the number of occurrences. Step 5: Use the equation to determine the probability assessment

Classical Probability Assessment Step by Step Process.

Step 1: Define the experiment Step 2: Determine whether possible outcomes are equalkly likely. Step 3: Determine the TOTAL number of outcomes. Step 4: Define the event of interest. Step 5: Determine the number of outcomes associated with the event of interest. Step 6: Use the equation to determine the probability assesment

Classical Probability Assessment.

The method of determining probability based on the ratio of the number of ways an event of interest can occur to the number ways any event may occur when each event is equally likely. P(E1) = number of ways E1 can occur / Total number of possible outcomes

Relative Frequency Probability Assessment

The method that defines probability as the number of times an event occurs divided by the total number of times an experiment is performed in a large number of trials. P(E1) = Number of times E1 occurs / N Where: E1 = The event of interest N = Number of Trials.

Subjective Probability Assessment.

The method that defines the probabilty of an event as reflecting a decision makers state of mind regarding the chances that the particular event will occur.

Independent Events

The occurrence of one event in no way influences the probability of the occurrence of the other event.

Conditional Probability

The probability that an event will occur given that another event has already occurred. Pr(A|B): probability of event A given that B has occurred.

Mutually exclusive Events

Two Events are Mutually Exclusive if the occurance of one event precludes the occurence of the other event. Or: two Events which cannot occur simultaniously.

Sample Space

When an experiment is conducted there are a specific number of possiblle outcomes . The range of possible outcomes of an experiment are known as the sample space.

Dependent Events

the occurance of one event impacts the probability of the occurance of the other event.