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Screen Shot 2020-05-29 at 11.30.41 AM Probability, ALGEBRA OF SETS, Notes…

- - - - 1 is certain to occur
      - 0 is impossible to occur
- - - - P(A) = # of time A occurred / # of times procedure was repeated
      - Example - flipping a coin for 10 times and observing it
  - - - P(A) = # of ways A occurs / # of different simple events = s/n
      - CAUTION When using the classical approach, always confirm that the outcomes
        are equally likely.
      - Example = flipping a coin or lottery prize, each combination has an equal chance of winning
- - - - all outcomes except "5" is a complement
- - - - Probability of event A occurring or
        event B occurring or
        they BOTH occurring in a SINGLE TRIAL
      - The word “or” in the addition rule is associated with
        the addition of probabilities.
      - = P(A) + P(B)
        works well for Mutually Exclusive
        
        For not Mutually Exclusive, Double Counting occurs.
        therefore, P(A or B) = P(A) + P(B) - P(A and B)
    - - Because events A and A must be
        disjoint, we can use the addition rule
        to express this principle as follows
  - - - Probability of A occurring and then B occurring in Successive Trials
- - - - The mean (or arithmetic mean) is generally the most important of all numerical measurements
        used to describe data, and it is what most people call an average.
    - - Range
        
        difference between maximum and minimum data value
      - Standard Deviation
        
        a measure of how much data values deviate away from the mean
        
        Notation
      - Variance
- - - - 3a. PERMUTATION -> when different sequence of the same items are counted counted separately. ORDER matters -
        WHEN ALL OF THE ITEMS ARE DIFFERENT
        
        n objects can be permuted in n! ways
        
        Without Replacement
      - 4. COMBINATION RULE -> counting no. of Different Arrangements possible when different sequence of the same items are counted same. ORDER DOES NOT matter
        
        we are counting the number of ways to choose k objects out of n, without replacement and without distinguishing between the different orders in which they could be chosen
        
        The binomial coefficient is sometimes called a combination
      - 3b. PERMUTATIO -> when different sequence of the same items are counted counted separately. ORDER matters -
        WHEN SOME ITEMS ARE IDENTICAL TO OTHERS