Probability Concepts Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Events and Probability An activity for which the outcome is uncertain is an experiment. An event consists of one more possible outcomes of the experiment. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Relative Frequency Approach Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Datacomp Survey M = a male is selected F = a female is selected U = the person selected is under 30 B = the person selected is between 30 and 45 O = the person selected is over 45 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Marginal Probability Marginal Probability the probability of a single event used to define the contingency table. P(M) = 120/200 =.6P(F) = 80/200 =.4 P(U) =.5P(B) =.25P(O) =.25 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Complement of an Event The Complement of an event A is the event that A does not occur.  P(A) + P(  ) = 1 P(M) = 1 - P(M) =.4 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Joint Probability The probability of the occurrence of two events at the same time. The probability of selecting a person who is a female and under 30 P(F and U) = 40/200 =.2 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Union of Events The Union of events is the probability of either event A or event B occurring. The probability of selecting a person who is Male or under 30. P(M or U) = ( ) / 200 =.8 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Conditional Probability Whenever you are given information and are asked to find a probability based on this information, the result is a Conditional probability. P(A|B) Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Independent Events If the P(A) = P(A|B) then event A is said to be independent of event B. P(M) = P(M|U) =.6 Thus event M is independent of event U. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Mutually Exclusive Events If an event can not occur when another event has occurred the two events are said to be Mutually Exclusive. Selecting a Male and a Female are mutually exclusive events. P(M|F) = 0 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Additive Probability Rules General Additive Rule P(A or B) = P(A) + P(B) - P(A and B) Special Additive Rule If A and B are mutually exclusive then: P(A or B) = P(A) + P(B) Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Conditional Probability Rules General Conditional Probability Rule P(A|B) = P(A and B) P(B)  0 P(B) Special Conditional Probability Rule If A and B are independent then: P(A|B) = P(A) P(A and B) = P(A) P(B) Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Tree Diagrams The probability of the event on the right side (say, event B) of the tree is equal to the sum of the paths; that is, all probabilities along a path leading to event B are multiplied, and then summed over all paths leading to B. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Figure 4.11 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Counting Rules Counting Rules determine the number of outcomes that exist for a certain broad range of experiments. Filling Slots Permutations Combinations Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Filling Slots Use counting rule 1 to fill k different slots. Let: n 1 = the number of ways to filling the first slot n 2 = the number of ways to filling the second slot after the first slot is filled  n k = the number of ways to filling the kth slot after slots 1 though k - 1 The number of ways of filling all k slots is: n 1  n 2  n 3  …  n k Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Permutations Permutations is the counting situation in which you select people without replacement and where order of selection is important. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Combinations Combinations is the counting situation in which you select people without replacement and where order of selection is not important. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing