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Class Note for MATH 1313 with Professor Flagg at UH 2

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This 5 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 20 views.

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Date Created: 02/06/15
Example 2 Suppose we toss a coin ve times and observe which side faces up after each toss What is the probability that exactly two tails occur Example 3 Suppose we toss a coin ve times Find the probability that it lands heads more than once Method 1 Method 2 Math 1313 Class Notes 7 Section 74 Page 2 of5 Example 4 Five cards are selected at random without replacement from a well shu led deck of 52 playing cards a Find the probability that at least one of them is a heart b Find the probability that 2 aces and 2 kings are chosen Note that the phrase at least one is a clue that you can use PE l PE Example 5 A department store receives a shipment of 100 computer games of which 6 are defective A customer buys 5 of these games What is the probability that a exactly 2 of them are defective b at least one of them is defective Math 1313 Class Notes 7 Section 74 Page 3 of5 c at most one of them is defective Example 6 From a group of 5 freshmen 6 sophomores 4 juniors and 3 seniors what is the probability that a staff of 3 freshmen 3 sophomores 2 juniors and 2 seniors will be selected for the yearbook staff Assume that each student is equally likely to be chosen Example 7 A fivemember committee is to be formed at random from a group of 7 Democrats and 9 Republicans Find the probability that the committee will consist of a two Democrats and three Republicans Math 1313 Class Notes 7 Section 74 Page 4 of5 b at most 4 Republicans c at least one Democrat Example 8 A class contains 30 students 18 girls and 12 boys A group of 5 students is chosen at random from the class to make a presentation to the school board What is the probability that the group making the presentation is made up of a more girls than boys b at least 1 boy c 2 or 3 boys Math 1313 Class Notes 7 Section 74 Page 5 of5 Math 1313 Section 74 Use of Counting Techniques in Probability Some of the problems we will work will have very large sample spaces or involve multiple events In these cases we will need to use the counting techniques from chapter 6 to help solve the probability problems In particular we ll work with the multiplication principle and combinations In this section we will look only at problems in which each outcome is equally likely The sample spaces for these types of problems are called uniform sample spaces Example 1 Suppose an experiment consists of tossing a coin three times and observing which side faces up after each toss a Describe the sample space for this event b What is the probability that HHH occurs c What is the probability that exactly two tails occur Suppose we tossed the coin ve times instead of three times The tree diagram and sample space would be too cumbersome to work with We ll use a different method Computing the Probability of an Event in a Uniform Sample Space nE nS 39 Let S be a uniform sample space and letE be any event Then PE Math 1313 Class Notes 7 Section 74 Page 1 of5

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