■ increase in demand for tech ■ growth of devices that depend on internet ○ à new system developed with 128 binary code sequences ● Permutations ○ Permutations – the number of different ways in which objects can be arranged in order ■ Number of permutations of n objects selected at X time can be found by Ni! ¸ (N-X)! ■ Ex: 3! = (3) • (2) • (1) = 6 ■ Can be found on calculator easily ○ Selecting Some (NOT all) Objects in a Group ■ Ex: 12 players on a team, how many diff ways can 5 players be selected? - Use formula [ N! ¸ (N – X)! ] ■ 12! ¸ (12 – 5)! à 12! ¸ 7! ● Combinations ○ Combinations – the number of different ways in which objects can be arranged
without regard to order ■ Order doesn’t matter, like in permutations ■ Number of combinations of n objects selected X at a time can be found by: N! ¸ [ (N – X)! • X! ] ■ N = total number of objects ■ X = the number of objects to be selected ○ Ex: 5 cards randomly selected from 52-card deck. How many 5-card combinations exist? ■ 52! ¸ (52 – 5)!5! ○ Ex: Probability of a flush – 5 cards of the same suit ■ Choose 5 same suit out of 13 same suit cards in a 52-card deck ■ 13! ¸ (13-5)!5! ○ Ex: Probability of Winning State Lottery ■ Pick 6 numbers out of a possible 49 ■ 49! ¸ (49-6)!6! ○ Probability does not have a memory ■ Selected chances have same probability of being selected again next time ■ b/c 2 events are independent and have no influence on one another ○ Combinations = useful in business ■ When a product or service is available with different options ● Permutation & Combination Functions ○ Permutation ■ =PERMUT (N,X) ○ Combination ■ =COMBIN (N,X) Chapter 5: Discrete Probability Distributions ● Chapter Intro ○ What is discrete data? ■ Values are typically whole numbers ■ Most situations never involve fractions ■ Counted values ○ Continuous Data ■ Measured ■ Can be any number, even fractions ○ Chapter Review ■ Determining discrete probabilities ■ Discrete probabilities – probabilities that describe the likelihood that certain discrete data will occur ■ Example: - Prices of pizzas, percentage of buyers that purchase (probability) - Number of test questions à probability of passing quiz given that you guessed all of them
■ Discrete Probabilities & Business - Forecasting customer demand to plan for staffing & inventory needs - Quantifying risk of producing defective items to provide better control of manufacturing process - Gauging diff customer satisfaction scores to improve customer service Ø 5.1 – INTRODUCTION TO DISCRETE PROBABILITY DISTRIBUTIONS o Business Experiments to Calculate Probabilities § Record number of customers who enter a store each hour during the day - à # customers entered in specific range § Randomly select 6 customers who walked into store & count the number who signed new cell phone contracts - 1/6 customers signed new cell phone contracts § Request that e/customer checking out of a hotel rate their satisfaction on a scale of 1-5 -
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- Fall '12
- Standard Deviation, Mean