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此概念图以 IHMC CmapTools 创建, 内含信息有关于: The fundemental of Probability, Probability measuring uncertainty ???? Permutations Number of ways in which objects can be arranged to give the desired outcome. Ordering of the objects mattes., Probability measuring uncertainty ???? Theoretical probability: This is found by considering equally likely evnets., Probability measuring uncertainty ???? Factorial notation Denoted by the exclamation mark: ! 6! is pronounced six factorial And 6!=6×5×4×3×2×1 Note: 0!=1, P(A) OR P(B) = P(A) +P(B) ???? ????, Expected value: For a particular event which has different possible outcomes, its expectation or expected value(EV) is a weighted average of the values associated with each possible out come ???? <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> EV= </mtext> <munderover> <sum/> <mtext> i=1 </mtext> <mtext> n </mtext> </munderover> <mtext> Pi ⋅Xi </mtext> </mrow> </math>, Combinations: Number of ways to select a set of objects from a total population, irrespective of the order. ???? <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> nCr= </mtext> <mfrac> <mtext> n! </mtext> <mtext> (n-r)! × r! </mtext> </mfrac> </mrow> </math>, Probability measuring uncertainty ???? Decision or probability tree: A decision or probability tree gives another format for visualising a problem involving probability, Probability measuring uncertainty ???? Combinations: Number of ways to select a set of objects from a total population, irrespective of the order., <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> Theoretical probability= </mtext> <mfrac> <mtext> number of ways an event can occur </mtext> <mtext> total number of different euqally likely enent that can occur </mtext> </mfrac> </mrow> </math> <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> Example:Rolling a dice and getting 
an even number has theoretical probability </mtext> <mfrac> <mtext> 3 </mtext> <mtext> 6 </mtext> </mfrac> </mrow> </math>, conditional probability: The situations where the probability of en event occurring depends in part on whether or not other events have already occurred. ???? <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> 
P(B|A) = Probability of event B, given that event A has already occurred.

P(C|AB)=Probability of event C, given that event A and B have already occurred.
P(B|A)={P(B)XP(A|B)}/P(A)
P(A|B)={P(A)XP(B|A)}/P(A) </mtext> </mrow> </math>, Theoretical probability: This is found by considering equally likely evnets. ???? <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> Theoretical probability= </mtext> <mfrac> <mtext> number of ways an event can occur </mtext> <mtext> total number of different euqally likely enent that can occur </mtext> </mfrac> </mrow> </math>, Expected value and decision trees: In a decision tree, the sequence of decisions and outcomes is represented graphically as the branches of the tree. At every point (or node) that a decision must be made or an outcome must occur, the tree branches out further until all the possible outcome have been displayed. ???? Circles (chance nodes): are used to indicate situation reflecting a ‘state of nature’, i.e., situations whose outcomes are not entirely under the conscious control of the decision maker., Expected value and decision trees: In a decision tree, the sequence of decisions and outcomes is represented graphically as the branches of the tree. At every point (or node) that a decision must be made or an outcome must occur, the tree branches out further until all the possible outcome have been displayed. ???? Boxed (decision nodes) are: used to indicate situation where the decision maker consciously selects a particular course of action (strategy) and where the outcome of that action is ‘certain’., Expected value and decision trees: In a decision tree, the sequence of decisions and outcomes is represented graphically as the branches of the tree. At every point (or node) that a decision must be made or an outcome must occur, the tree branches out further until all the possible outcome have been displayed. ???? Pay-offs : are the valuations placed at the end of particular branches emanating from chance nodes. They are the values which are allocated to that event or outcome should it occur., Probability measuring uncertainty ???? Venn diagram for non-mutually exclusive events, Probability measuring uncertainty ???? conditional probability: The situations where the probability of en event occurring depends in part on whether or not other events have already occurred., Independent event: one event has no effect onanother event ???? P(A) and P(B)=P(A)XP(B), Venn diagram for non-mutually exclusive events ???? ????, Mutually exclusive envents: If one event excludes the possibility of another envent happening, then we say that the two envets are mutually exclusive ???? P(A) OR P(B) = P(A) +P(B), Decision or probability tree: A decision or probability tree gives another format for visualising a problem involving probability ???? ????