ACMS10145 Lecture Notes - Lecture 4: Sample Space
28 Aug 2020
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● Probability is a numerical measure of the likelihood that an event will occur
○ Probability = 0, event is not likely to occur
○ Probability = 1, event is likely to occur
● Experiment: act or process of watching that leads to a single outcome that cannot be
predicted with certainty. Can be either complex or simple
● Sample point: the most basic outcome of an experiment, and the sample space is the
collection of all its sample points
● Event: outcome of interest, specific collection of sample points
● Sample space: a collection of all possible outcomes of an experiment
● Multiplication principle: (die example)
○ An experiment 1 has n1 outcomes and for each of these outcomes an experiment 2
has n2 possible outcomes. The composite experiment 1x2 has (n1)(n2) possible
outcomes
○ # of possible outcomes: (outcomes for 1)(possible outcomes for2)
● Permutation: each of the n! arrangements of n different objects (order matters)
○ If we only need r positions filled and n≠r, possible arrangements are:
○ If n=r, n!=n(n-1)(n-2)....1
○ Calculator pathway: math, prob, 2(nPr)
● Combination: ordered sample without replacement (order doesn’t matter)
○ Combination of n objects taken r at a time
○ Calculator: math, prob, 3 (nCr)
○ nCr = nCn-r
● Basic requirements for assigning probabilities:
○ The probability assigned to each experimental outcome must be between 0 and 1,
inclusively
○ The sum of all the probabilities for all the experimental outcomes must be 1
Document Summary
Probability is a numerical measure of the likelihood that an event will occur. Probability = 0, event is not likely to occur. Probability = 1, event is likely to occur. Experiment: act or process of watching that leads to a single outcome that cannot be predicted with certainty. Sample point: the most basic outcome of an experiment, and the sample space is the collection of all its sample points. Event: outcome of interest, specific collection of sample points. Sample space: a collection of all possible outcomes of an experiment. An experiment 1 has n1 outcomes and for each of these outcomes an experiment 2 has n2 possible outcomes. The composite experiment 1x2 has (n1)(n2) possible outcomes. # of possible outcomes: (outcomes for 1)(possible outcomes for2) Permutation: each of the n! arrangements of n different objects (order matters) If we only need r positions filled and n r, possible arrangements are: Combination: ordered sample without replacement (order doesn"t matter)
