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Lecture #9 - Laws of Probability.doc

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Jeff Racine

Lecture # 9- Chapter 4 and 5 (Part 3) Laws of Probability: Addition (Beginning of Lecture #9) • The General Addition Law (probability of the union) o The probability of event A or B happening equals the probability of A occurring alone plus the probability of B occurring alone minus the probability of A and B happening at the same time p(A U B)= p(A)+ p(B) - p(A B) • The Special Addition Law (probability of mutually exclusive events) o When dealing with mutually exclusive events, no intersection is possible. Ie: the outcome must be either A or B. In this instance: p (A U B)= p(A)+ p(B) o Add A + B o The area in the middle is counted subtract the area in the middle from the 2 circles Example (Consider a deck having 52 cards (12 are “face cards” Ie: J, Q, K for each of four suits), and you draw one card) • The probability of event A (getting a face card) us the sum if the probabilities of drawing any of the 12 face cards (1/52), hence (special addition law) p(A)= 1/52 + 1/52 +…..+ 1/52=12/52 Laws of Probability: Multiplication • Unconditional Probability p(A) o The likelihood that a particular event will occur, regardless of whether another event occurs • Joint Probability p(A B) o The likelihood that two or more events will occur simultaneously (ie: probability of the intersection, probability of A and B) • Conditional Probability p(A|B)= p(A B)/ p(B) o The likelihood that a particular event occurs, given the fact that another event has already occurred or is certain to occur. o p(A|B)= probability of A given B • Unconditional Joint Probability Rule p(A)= p(A B): o We will be given a number of joint probabilities, and if you want to use those joint probabilities to recover an unconditional probability you must add the appropriate joint probability over the other variable: Example (Unconditional, conditional, joint probability) • The probability of drawing a heart (event B)
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