Probability and Probability and Simulation Simulation The Study of RandomnessThe Study of Randomness

Probability Probability Probability is the Probability is the

branch of branch of mathematics that mathematics that

describes the describes the pattern of chance pattern of chance

outcomes. outcomes.

Probability JargonsProbability JargonsExperimentExperiment: process of measuring or observing : process of measuring or observing an activity for the purpose of collecting data. an activity for the purpose of collecting data. Ex: rolling a pair of diceEx: rolling a pair of diceOutcomeOutcome: A particular result of an experiment. : A particular result of an experiment. Ex: rolling a pair of threes with the dice.Ex: rolling a pair of threes with the dice.Sample Space:Sample Space: All possible outcomes in an All possible outcomes in an experiment. Ex: sample space of a die {1, 2, 3, experiment. Ex: sample space of a die {1, 2, 3, 4, 5, 6}4, 5, 6}EventEvent: One or more outcomes that are of : One or more outcomes that are of interests for the experiment. Ex: rolling a total interests for the experiment. Ex: rolling a total of 2, 3, 4, or 5 with 2 diceof 2, 3, 4, or 5 with 2 dice

Basic Set NotationsBasic Set NotationsSuppose that you roll a die once. There will be 6 possible outcomes; you may get either 1, 2, 3, 4, 5 or 6. These possible outcomes of such a random experiment are called the basic outcomes. The set of all basic outcomes is called the sample sample space.space. The symbol SS will be used to denote the sample space.

SS = sample space = sample space

What is the sample space for a roll of a single six-sided die?

S = {1, 2, 3, 4, 5, 6}

What is the sample space for tossing a coin?

S = { T, H}

Classical ProbabilityClassical ProbabilityRefers to the situation when we Refers to the situation when we know the number of possible know the number of possible outcomes of the event of interest outcomes of the event of interest and can calculate the probability of and can calculate the probability of that event.that event.

P[A]=P[A]=Number of possible outcomes in which EVENT A Number of possible outcomes in which EVENT A

occursoccursNumber of possible outcomes in the SAMPLE SPACENumber of possible outcomes in the SAMPLE SPACE

Event A = rolling a total of 2, 3, 4, or Event A = rolling a total of 2, 3, 4, or 55

P[A]=?P[A]=? A = 10A = 10S = 36 S = 36

P[A]= 10/36P[A]= 10/36= 0.28= 0.28

ClassworkClasswork

Find the Probability of the following eventsFind the Probability of the following eventsA = same numberA = same numberB = both odd numberB = both odd numberC = sum of 7, 8, 9, or 10C = sum of 7, 8, 9, or 10

D = an odd and an even numberD = an odd and an even numberE = not getting a sum of even E = not getting a sum of even numbernumber

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