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
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
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
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
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
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
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
Permutations A permutation is an arrangement of n objects in a specific order .

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