Chapter 6

Chapter 6 - Chapter 6: Probability Basic Rules of...

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Chapter 6: Probability Basic Rules of Probability Probability – measure of how likely it is that something will occur Experiment – any action whose outcomes are recordable data. Sample Space – S, set of all possible outcomes of an experiment Could have a finite number of elements (countable) Could have an infinite number of elements (when the data from the experiment are quantitative and continuous. Event, A – outcome or set of outcomes that are of interest to the experimenter Probability of an Event A, P(A) – a measure of the likelihood that an event A would occur. P(A) = Number of ways that A can occur Total number of possible outcomes P(A) = n A N Facts About Probabilities that Must be True: 1. 0 ≤P(A)≤1.  This says that the probability of an event must be a number  between 0 and 1 inclusive. Since you know that probabilities are formed  by taking the ratio of the number of ways that A can happen to the total  number of outcomes, the numerator is a subset of (smaller than or equal  to) the denominator. 2. P(S) = 1. This says that the sum of probabilities for the entire sample  space must be equal to 1, or that essentially when you perform an  experiment, something must happen. 3. If an event A  must  happen, then P(A) = 1, and if the event cannot happen,  then P(A) = 0. Complement –  the complement of an event A, denoted A’, is the set of all  outcomes in the sample space, S, that did not correspond to the event A. P(A) + P(A’) = 1 P(A) = 1 – P(A’) Combinations of Events: OR and AND A OR B –  describes the event when either A happens or B happens or  they both happen A AND B – describes the event that A and B both occur Mutually Exclusive – two events, A and B, are said to be mutually exclusive if they have no outcomes in common Simple Addition Rule:

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P(A OR B) = P(A) + P(B) The simple addition rule easily extends to any number of mutually exclusive events. P(A OR B OR C OR D) = P(A) + P(B) + P(C) + P(D) The word OR is inclusive. General Addition Rule P(A OR B) = P(A) + P(B) – P(A AND B) Empirical Probabilities – one that is calculated from sample data and is an estimate for the true probability Relative Frequencies (Page 234) Conditional Probability and Independence Conditional Probability o Written as P(A|B) o Read “the probability that A will occur given that B has occurred” or “the probability of A given B” o One that is calculated from a reduced sample space. P(A|B) = P(A AND B) P(B) Independent Events – the probability that one event occurs on any given trial of an experiment is not affected or changed by the occurrence of the other event P(A|B) = P(A) Two events are independent exactly when: P(A AND B) = P(A) x P(B) (The phrase exactly when means that the statement can be used in both directions. If we
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This note was uploaded on 04/18/2008 for the course ECON 205 taught by Professor Diagne during the Fall '07 term at Towson.

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Chapter 6 - Chapter 6: Probability Basic Rules of...

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