QBA237Chapter4.pdf - Chapter 4 Introduction to Probability QBA 237 Basic Business Statistics Raju Mainali Summer 2020 Outline 4.1 Random Experiments

QBA237Chapter4.pdf - Chapter 4 Introduction to Probability...

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Chapter 4. Introduction to Probability QBA 237 Basic Business Statistics Raju Mainali Summer 2020
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Outline 4.1 Random Experiments, Counting Rules, and Assigning Probabilities 4.2 Events and Their Probabilities 4.3 Some Basic Relationship of Probability 4.4 Conditional Probability 1
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Basic Ideas I An experiment is a process of making an observation when there is uncertainty about which of two or more possible outcomes will result. Experiment Experiment Outcomes Tossing a coin Head, tail Rolling a die 1,2,3,4,5,6 Inspection a part Defective, non-defective Play a football game Win, lose, tie I The set of all possible outcomes of an experiment is called the sample space for the experiment. The sample space is denoted as S . 2
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Example 1 I Find a sample space of throwing a die. S = { 1 , 2 , 3 , 4 , 5 , 6 } I Find a sample space of tossing a coin. S = { H , T } I Find a sample space of tossing two coins simultaneously. S = { HH , HT , TT } ( HT = TH ) I Find a sample space of tossing two coins in turn. S = { HH , HT , TH , TT } ( HT 6 = TH ) 3
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Example 1 (cont’d) I Suppose a box contains three balls, one red, one blue, and one white . One ball is selected, its color is observed, and then the ball is placed back in the box. The balls are scrambled, and again, a ball is selected and its color is observed. What is the sample space of the experiment? S = { RR , RB , RW , BR , BB , BW , WR , WB , WW } 4
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Counting Methods When computing probabilities, it is sometimes necessary to determine the number of outcomes. For example, a car is available in any of three colors: red, blue, or green, and comes with either a large or small engine. In how many ways can a buyer choose a car? S = { (R, L), (R, S), (B, L), (B, S), (G, L), (G, S) } . The total number of choices is 6. 5
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Fundamental Principle of Counting In a sequence of n events in which the first one has k 1 possibilities and the second event has k 2 and the third has k 3 , and so forth, the total number of possibilities of the sequence will be k 1 × k 2 × · · · × k n Example ) A restaurant offers a special dinner menu every day. There are ten entrees, eight appetizers, and seven desserts to choose from. A customer can only select one item from each category. How many different meals can be ordered from the special dinner menu? 6
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Permutations A permutation is an arrangement of n objects in a specific order .
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