Lesson_03_Notes - Probability

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Probability Introduction Learning objectives for this lesson Upon completion of this lesson, you should be able to do the following: determine which general probability rules to apply to a given situation properly apply the general probability rules Probability First, consider the notation P(A) represents the notation "Probability event A occurs and P(A c ) represents the "probability that the complement of event A occurs" where the complement of an event is simply any event that is not event A. An example would be if you allow for only three political party affiliations: Republican, Democrat, and Independent, then P(A) could represent the probability of being an Independent, P(Independent), and P(A c ) would represent the probability of "not being an Independent", P(Republican or Democrat). You can see how knowing this notation makes for a much more simple expression! General Probability Rules Rule 1: The probability of an impossible event is zero; the probability of a certain event is one. Therefore, for any event A, the range of possible probabilities is: 0 ≤ P(A) ≤ 1 Rule 2: For S the sample space of all possibilities, P(S) = 1. That is the sum of all the probabilities for all possible events is equal to one. Recall the party affiliation above: if you have to belong to one of the three designated political parties, then the sum of P(R), P(D) and P(I) is equal to one. Rule 3: For any event A, P(A c ) = 1 - P(A). It follows then that P(A) = 1 - P(A c ) Rule 4 (Addition Rule): This is the probability that either one or both events occur a. If two events, say A and B, are mutually exclusive - that is A and B have no outcomes in common - then P(A or B) = P(A) + P(B) b. If two events are NOT mutually exclusive, then P(A or B) = P(A) + P(B) - P(A and B) Rule 5 (Multiplication Rule): This is the probability that both events occur a. P(A and B) = P(A)*P(B|A) or P(B)*P(A|B) Note: this straight line symbol, |, does not mean divide! This symbols means "conditional" or "given". For instance P(A|B) means the probability that event A occurs given event B has occurred. Probability http://onlinecourses.science.psu.edu/stat200/book/export/html/28 1 of 7 9/27/2010 11:45 PM
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b. If A and B are independent - neither event influences or affects the probability that the other event occurs - then P(A and B) = P(A)*P(B). This particular rule extends to more than two independent events. For example, P(A and B and C) = P(A)*P(B)*P(C) Rule 6 (Conditional Probability): P(A|B) = or P(B|A) = Conditional Probability In the lesson on Examining Relationships we found conditional distributions from two-way tables [for example, to find the percentage of students who did not smoked cigarettes given gender was female was 94.5%]. Now, we will solve for
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This note was uploaded on 10/08/2010 for the course STAT 200 taught by Professor Barroso,joaor during the Fall '08 term at Penn State.

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Lesson_03_Notes - Probability

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