Introduction to Probability

The study of descriptive statistics was concerned with what has occurred, probability is concerned with what will occur. Many of the concepts are the same, although some of the vocabulary changes. Descriptive statistics is concerned with (relative) frequency in the past, probability with (relative) frequency in the future.


something which generates an outcome (e.g., pick a card, roll a die, weigh a student, look outdoors)
Outcome (also called simple event)
result of an experiment (e.g., jack of spades, 3 pips, 145 pounds, partly cloudy)
Sample space (denoted by S)
set of all possible outcomes of an experiment (e.g., for picking a card there are 52 possible outcomes, hence 52 points in the sample space)
a set of outcomes, or equivalently, a subset of the sample space (e.g., for picking a card, events include getting a spade, getting a deuce, getting a face card)
N.B.: Sometimes identifying outcomes is subtle. If you roll a pair of dice, is the total number of pips, the pair of values on the two dice, or the ordered pair of values on the two dice the outcome?


A probability space entails that a probability be assigned to each outcome.

Where do probabilities come from?

Competencies: Given the following (incomplete) table of probabilities associated with rolling an unfair die:
   o_i |  1  |  2  |   3  |  4  |  5  |  6  |                                   
   p_i | .2  | .1  |  .3  | .1  |  ?  | .1  |                                   
What is the probability of rolling a 5?
What is the probability of rolling an even number (2 or 4 or 6)?

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