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The intersection of events A and B is the set of all

4.3.3 Intersection of Two Events. The intersection of events A and B is the set of all sample points that are in both A and B. The intersection of events A and B is denoted by A   . Sample Space S. Event A. Event B. Intersection of A and B.

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The intersection of events A and B is the set of all

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  1. 4.3.3 Intersection of Two Events The intersection of events A and B is the set of all sample points that are in both A and B. The intersection of events A and B is denoted by A Sample Space S Event A Event B Intersection of A and B

  2. Example: Intersection of Two Events Event M = Markley Oil Profitable Event C = Collins Mining Profitable MC = Markley Oil Profitable and Collins Mining Profitable MC = {(10, 8), (5, 8)} P(MC) =P(10, 8) + P(5, 8) = .20 + .16 = .36

  3. Addition Law The addition law provides a way to compute the probability of event A, or B, or both A and B occurring. The law is written as: P(AB) = P(A) + P(B) -P(AB

  4. Example: Addition Law Event M = Markley Oil Profitable Event C = Collins Mining Profitable MC = Markley Oil Profitable or Collins Mining Profitable We know: P(M) = .70, P(C) = .48, P(MC) = .36 Thus: P(MC) = P(M) + P(C) - P(MC) = .70 + .48 - .36 = .82 (This result is the same as that obtained earlier using the definition of the probability of an event.)

  5. 4.3.4 Mutually Exclusive Events Two events are said to be mutually exclusive if the events have no sample points in common. Two events are mutually exclusive if, when one event occurs, the other cannot occur. Sample Space S Event A Event B

  6. Mutually Exclusive Events If events A and B are mutually exclusive, P(AB= 0. The addition law for mutually exclusive events is: P(AB) = P(A) + P(B) there’s no need to include “- P(AB”

  7. ??? 4.4 Conditional Probability The probability of an event given that another event has occurred is called a conditional probability. The conditional probability of A given B is denoted by P(A|B). A conditional probability is computed as follows :

  8. = Collins Mining Profitable given Markley Oil Profitable Example: Conditional Probability Event M = Markley Oil Profitable Event C = Collins Mining Profitable We know: P(MC) = .36, P(M) = .70 Thus:

  9. Multiplication Law The multiplication law provides a way to compute the probability of the intersection of two events. The law is written as: P(AB) = P(B)P(A|B)

  10. Example: Multiplication Law Event M = Markley Oil Profitable Event C = Collins Mining Profitable MC= Markley Oil Profitable and Collins Mining Profitable We know: P(M) = .70,P(C|M) = .5143 Thus: P(MC) =P(M)P(M|C) = (.70)(.5143) = .36 (This result is the same as that obtained earlier using the definition of the probability of an event.)

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