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The Math Learning Portfolio Casino: Test Your Luck

Probability Laws
Four Probability Properties
Pascal's Wager and Bernoulli Trials
John Forbes Nash and Game Theory
Chance Games
Math in Music
Demonstration of Goals

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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