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Test #2 cheat sheet

Test #2 cheat sheet - Definitions Probability experiment An...

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Definitions Probability experiment - An action, or trial, through which specific results (counts, measurements, or responses) are obtained. Outcome - The result of a single trial in a probability experiment. Sample Space - The set of all possible outcomes of a probability experiment. Event - Consists of one or more outcomes and is a subset of the sample space. Simple event - An event that consists of a single outcome (An event that consists of more than one outcome is not a simple event). Fundamental Counting Principle - If one event can occur in m ways and a second event can occur in n ways, the number of ways the two events can occur in sequence is m*n . Can be extended for any number of events occurring in sequence. Law of Large Numbers - As an experiment is repeated over and over, the empirical probability of an event approaches the theoretical (actual) probability of the event. Subjective Probability - Intuition, educated guesses, and estimates. Range of probabilities rule - The probability of an event E is between 0 and 1, inclusive. 0 ≤ P(E) ≤ 1 Complement of event E (E') - The set of all outcomes in a sample space that are not included in event E . Denoted E ′ ( E prime). P ( E ′) + P ( E ) = 1 Permutation - An ordered arrangement of objects. The number of different permutations of n distinct objects is n ! ( n factorial). n ! = n ∙( n 1)∙( n – 2)∙( n – 3)∙ ∙ ∙3∙2 ∙1; 0! = 1 n P r Ex There are 15 dogs entered in a show. How many ways can first, second, and third place be awarded? N=15 R=3 15 P 3 15!/(13-3)!= 3,730 ways Combination of n objects taken r at a time - A selection of r objects from a group of n objects without regard to order n C r Ex There are 13 students in a club. How many ways can four students be selected to attend a conference? N=13 R=4 13 C 4 13!/(13-4)! (4!)= 715 ways Formulas Classical (theoretical) Probability - Each outcome in a sample space is equally likely. Empirical (statistical) Probability - Based on observations obtained from probability experiments. The relative frequency of an event. 4! (4*3*2*1)=24 How many 4 letter TV call signs are possible, if each sign must start with either a K or W? 1 st letter=2 (K or W) 2 nd letter=26 3 rd letter=26 4 th letter=26 2*26*26*26=35,152 possibilities.

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