oct 28 quiz - Topic Name Delonta Holmes Teacher William...

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Topic Name: Delonta Holmes Teacher: William Hawk Class: Critical Thinking Date 10/26/09 Questions/Main Ideas: Notes Probability Calculations Cogent Inductive Arguments Provide Probability Deductive probability Scale: 0 = event will not happen 1 = event will happen between 0 & 1 = probability Theories of Probability Relative Frequency Theory – based on empirically determinate statistics Subjective Theory – based on personal beliefs and experience General Conjunction Rule Used to calculate the probability of two or more dependent events. Dependent events = the occurrence of one has an effect on the probability of the other. P(A) x P(A given B) x P(N given A through N-1) Example: Drawing two aces from a deck P = 4/52 x 3/51 = 12/1652 = .0045248% Restricted Disjunctive Rule Used to calculate two or more mutually exclusive events. P(A or B or N) = P(A) + P(B) +…P(N) Example: Rolling a 4 or 6 on a die P(4 or 6) = 1/6 + 1/6 = 1/3 = .3333% General Disjunction Rule Used to calculate that either of two or more events will occur. P(A or B or…N) = [P(A) + P(B) + …P(N)] – [P(A X B X …N)] P(A or U) = (.63 + .52) – (.63 x .52) = (1.15 - .3276) = .8224 Negation Rule Tells the probability an event will occur given the probability that it will not occur. P(A) = 1 - P(Not-A) Example: That aunt [.63] will die before 80 P(D) = 1 - .63 = .37 Conditional Probability Calculating the probability of B given A P(A) Example: Probability of drawing King if a face card has been drawn P(K/F) = 4 = .3334 12 Generalizations and Particularizations Invalid Argument Assessed in terms of strength Possible that the premises are true and the conclusion is false. Generalization Argument concerning a population based upon observation of a “representative” sample. Strength of inductive argument Depends upon modesty of conclusion. Depends upon the size of the sample. Depends upon the diversity of the sample. Depends upon the degree to which the sample is representative of the population Particularization Drawing inferences about a subset of a group based upon facts concerning the entire population of that group. Form of Particularization Arguments Where n is a number between 0 and 100, and x is kind of thing, and P is some property or relationship: 1. n percent of x ’s have P
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2. A is an x 3. Thus, there is an n * percent probability that A has P (where n * is less than or equal to n ) Analogical Arguments Form of Analogical Arguments 1. Objects x , y , z …all have properties P , Q , R , S 2. Object w also has properties Q , R , S 3. Thus, (probably) object w also has P . Evaluating Analogical Arguments: Stronger Analogical Arguments Have More . .. 1.
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oct 28 quiz - Topic Name Delonta Holmes Teacher William...

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