Basic Probability

Definitions

a priori Probability: the probability that we determine from knowing the process by which the uncertain event happens (by logically examining existing information).

Certain Event: event that is sure to happen (Probability = 1).

Chance: see "Probability [1]."

Collectively Exhaustive Events: (a.k.a. jointly exhaustive events) at least one of the events must occur.

Combination: a selection of a part of a set of objects, without regard to the order in which the objects are selected.

Complement: a complement of a set A refers to things not in A.

Conditional Probability: the probability of an event ( A ), given that another event ( B ) has occurred.

Contingency Table: a table/matrix that displays the frequencies of the joint events or the (joint) probabilities of the joint events.

Empirical Probability: (a.k.a. experimental probability) the ratio of the number of outcomes in which a specified event occurs to the total number of trials, not in a theoretical sample space but in an actual experiment.

Experimental Probability: see "Empirical Probability."

General Addition Rule: P(A or B) = P(A) + P(B) - P(A and B).

General Multiplication Rule: P(A and B) = P(A|B)P(B).

Impossible Event: event that is sure not to happen (Probability = 0).

Independent Events: two events are independent iff P(A|B) = P(A).

Joint Probability: probability of an occurence involving two or more events.

Likelihood: see "Probability [1]."

Marginal Probability: the probability of one variable taking a specific value irrespective of the values of the others.

Mutually Exclusive Events: events are mutually exclusive if they cannot occur at the same time.

Odds: see "Probability [1]."

Permutation: a selection of a part of a set of objects, with regard to the order in which the objects are selected..

Probability [1]: (a.k.a. chance, odds, likelihood) likelihood that an uncertain event will occur.

Probability [2]: a numerical measure of the likelihood that an uncertain event will occur. It is an index number between 0 and 1, larger number meaning greater likelihood.

Sample Space: the set of all possible outcomes or results of an experiment.

Statistical Independence: see "Independent Events."

Subjective Probability: a probability derived from an individual's personal judgment.

Uncertain Event: an event that may or may not occur (and you don't know whether it will occur or not).

Venn Diagram: shows the sets in pictures where each circle represents the mebers of a particular set.

Notes

I would like you to take these to heart:

• the probability is an index in between 0 and 1;
• it has no units of measurement;
• probability of an impossible event is 0;
• probability of a certain event is 1;
• the greater is the likelihood of abn ancertain event happening, the greater is the magnitude of the probability index (e.g., if probability of A is 0.8 and probability of B is 0.65, A is more likely to happen than B);
• this index is a ratio X/N, where X is the number of ways an event can happen out of N possible outcomes;
• determining the probability of an event always implies some process.

Read These

Chapter 4. Organizing and Visualizing Variables in the textbook:

4.1 Basic probability Concepts (pp. 152-159)

• You will benefit a lot from doing as many exercises as you can on pp. 159-161.

4.2 Conditional Probability (pp. 161-163, 165-167)

• You may omit the section "Decision Trees."

4.3 Bayes' Theorem (pp. 169-170)

• Try to find other discussions (AC library, Internet, etc) of the Bayes' Theorem. Most people find it counter-intuitive, so it is harder than other things to understand/remember/use.
• You may omit the "decision trees" explanation. Or try to work through it. I will not use these "decision tree" approaches for any questions in the tests.

4.4 Counting Rules (pp. 174-176)

• Memorize the formulae.
• We will use some of the formulae very soon, for the discrete distributions. It should help your recall.

You may omit section 4.5 Ethical Issues and Probability

Watch This

Answer These

Do problem 4.1 (p. 159 in the textbook).

Do problem 4.7 (p. 159 in the textbook).

Do problem 4.13 (p. 161 in the textbook).

Do problem 4.25 (p. 169 in the textbook).

Do problem 4.32 (p. 173 in the textbook).

And it is probably a good idea to answer every problem on pages 176-177. They are short, and they will help you get accustomed to using the counting rules.