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Probability by Mind Map: Probability
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Probability

The proportion of times something would occur over the long run.

Random Circumstance

outcome not determined until we see it

Outcome already determined but our knowledge is uncertain

Relative Frequency Interpretation

Make assumption about Physical world

Make direct observation of how often something happens over many, many repetitions of the situation.

Number between 0 and 1

The possible outcome of a random circumstance

Meets 1st condition for valid probablity

Personal Probability (subjective)

Degree an individual believes it will happen

Coherent (no contradiction)

Uses percentages based on proportions of individuals

Definitions

Sample Space

With Replacement

Without Replacement

Simple Event

Sum of all Simple Events = 1

If equally likely then probability = 1/k

Event

Events

Complementary ("Opposite")

mutually exclusive (disjoint)

Independent

Dependent

Conditional Probablity

P(B|A) = probability of B given A

Rules for Finding Probabilities

Rule 1 (Not the event)

Probability an event does not occur, P(A)+P(A^c)=1

Rule 2 (Addition)

Probability that either of two events happens, Rule 2a (general), P(A or B)=P(A)+P(B)-P(A and B), Rule 2b (mutually exclusive events), P(A or B)=P(A)+P(B)

Rule 3 (Multiplication)

Probability that two or more events occur together, Rule 3a (general), P(A and B)=P(A)PB|A)=P(B)PA|B), Rule 3b (independent events), PA and B)=P(A)P(B), Rule 3b (extension), P(A1 and A2...and An)=P(A1)P(A2)...(PAn)

Rule 4 (Conditional Probability)

Determining a conditional probability, P(B|A)=P(A andB)/P(A)

Philosophical Issue

Outcome has been determined but is still unknown

Confidence vs Probability

Strategies

Bayes Rule

P(A|B)=P(A and B)/PB|A)P(A)+P(B|A^c)P(A^c)

Two-way Tables: Hypothetical 100,000

Tree Diagram