Unit 4: Probability Basics

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21 Terms

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Probability

long run of relative frequencies; between 0 & 1;

  • short term—>unpredictable

  • long term—>predictable

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Law of Large Numbers

If we do something many many times, the results will start to match the expected probability more closely

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Simulation

imitation of chance behavior based on a model that accurately reflects the situation (dice, flip a coin, applets, random # generator)

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Simulation process

  1. Describe how you simulate 1 trial (one repetition)

  2. Perform many trials

  3. Use the results to answer the question

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Mutually exclusive

can’t occur together

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complement

probability of an event not happening (Ac)

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Random Process

all possible outcomes that can occur are known, but individual outcomes are unknown; generates results that are determined by chance

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Outcome

result of a trial of a random process

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Event

collection of outcomes

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Sample Space

collection of all possible non-overlapping outcomes

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Adding/substracting a constant c

shape: same; center: ± by c (mean & median); variability: same (if there is an equation that says to add or subtract to find the sd, don’t do it)

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Multiplying/Dividing a constant c

shape: same; center: multiple/divide by c (mean and median); variability: multiply/divide by c

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BINS

binary: each trial is a success or failure; independent: each trial is independent of each other; number of trials: fixed; same probability of success for each trial

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Interpreting Mean

after many many trials, the average # of success context is mean out of n

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Interpreting SD

the number of success context typically varies by SD from the mean of ___ out of n

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10% condition

When taking a random sample (w/o replcement) of size n from a population of size N we can use a binomial distribution if n<1/10N

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Large Counts Condition

allows us to use normal distribution to model a normal distribution if np>=10 and n(1-p)>=10

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Geometric: BITS

binary: each trial is a success or failure; independent: each trial is independent of each other; trials until first success occurs (not fixed); same probability of success for each trial

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Describing Geometric Distributions

shape: always skewed to the right

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random variable

a random process whose outcomes are numerical values

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discrete random variable (x)

takes a fixed number of values with gaps between values