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Statistics

9/20/2016

Probability

The probability is a measurement of the chance

The probability is a number between 0 and 1, corresponding to 0% and 100%

Definitions

Experiment – A process (game) that lead to an outcome as observation that cannot be

predicted. (i.e. random outcome)

Sample Point – The most basic outcomes of an experiment. The sample points MUST be

mutually exclusive from each other.

Sample Space – The collection of all possible sample points.

Event – A specific collection of sample points which have a common property. An event

can be a subset of the sample space. The sample is also an event.

oImpossible event – The event that won’t happen ever. This will be an empty set

that contains no sample points.

oCertain Event – The event that will happen for sure. The sample space is a certain

event.

Notation

Events: Capital letters such as A, B, C…

oA = {Event description}

Probability: P

oP(A) = Probability / chance that A will happen

Impossible Event: Phi (Fee)

Sample Space – S

P() = 0, and P(S) = 1

Properties of the Probability

The probability is a number measuring the chance. A number to be a probability needs

to satisfy the following:

oThe probability is a non-negative number and can be no larger than one, i.e. the

probability p satisfies 0<P<1

oThe total of probabilities of all sample points ins 1, i.e. the possibility of all

possible cases together. For example, in a sample space S, there are 5 sample

points; E1, E2, E3, E4, E5 thus P(E1) +P(E2) +P(E3) +P(E4) +P(E5) =1. Because the

total event of all possible sample points covers all possible results.

How to Compute Probability

Relative Frequency Approach

oRepeat the game as many times as you can, see how many times you win the

game (frequency fi winning the game). Divide by the total number of your trials.

oThe relative frequency approach is an approximation to the probability of

winning the game; when you enlarge the number if trials the approximation can

be improved.

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