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The Math Learning Portfolio Casino: Test Your Luck

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Probability Laws
Four Probability Properties
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John Forbes Nash and Game Theory
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Four Probability Properties

Four Probability Properties:

Probability is the measurement of the likelihood of an occurrence of an event. The unit of measurement is from 0% to 100%.

Key terms:

Relative Frequency is the average rate of incidence of an event in a number of trials.

Personal Probability is one’s level of belief that an event will arise.

 

Methods of Determining Probability:

Empirical Method: P (event x) = (# of times x occurred) (# of trials)

*note: more trials will result in a more accurate estimation

 

Equally Likely Outcomes

The previous rules are based on assuming that events x and y are equally likely.

 


Theoretical Method: Make mathematical hypotheses to determine probability of an event.

The four properties of probability:

1. Event occurs.

P (x occurs) + P (x does not occur) = 1

 

2. Occurrence at different times; when x and y occur at different times.

P (either x or y occurs) = P(x occurs) + P(y occurs)

 

3. X and y are independent. Y is not more likely to happen when A happens than when A does not happen.

P(x and y both occur) = P (x occurs) * P (y occurs)

 

4. Other influxes. When x occurs, y has to occur, too.

P (x occurs) <= P (y occurs)

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