# Probability and Statistics Fall 2018-2019_Lecture 5.pdf -...

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Arab Academy for Science, Technology & MaritimeTransportStatistics & Probability(BA329 – BA203)Lecture 5: Probability: (Counting Rules)Dr. Mohamed FathySpring 2018 – 2019
Chapter 2ProbabilityCounting RulesIn many of the examples in this chapter, it is easy to determine the number of outcomes ineach event. In more complicated examples, determining the outcomes in the sample space (or anevent) becomes more difficult. Instead, counts of the numbers of outcomes in the sample spaceand various events are used to analyze the random experiments. These methods are referred toascounting rules. Some simple rules can be used to simplify the calculations.Counting Rule 1If any one of𝑘different mutually exclusive and collectively exhaustive events can occur on eachof𝑛trials, the number of possible outcomes is equal to𝑘𝑛Example 2.30Suppose you toss a coin five times. What is the number of different possible outcomes(the sequences of heads and tails)?
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Example 2.31Suppose you roll a die twice. How many different possible outcomes can occur?.
Example 2.32In how many different ways can you seat 8 people in row at a dinnertable?

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