1324Winter2004Chapter6and7Lecture_Examples - Math 1324...

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Unformatted text preview: Math 1324 Probability 6.2 SETS AND COUNTING TECHNIQUES Read section 6.2 from the text before beginning this document. This document does not explain all of the topics from section 6.2 (Sets). From section 6.2, note the following definitions: • A is an element of B { A ∈ B) • The empty set. ∅ • Set Notation • Subset, {A ⊂ B}, and Not a Subset {A ⊄ B} • Equal To {A=B} and Not Equal To {A≠B} • Union {A ∪ B}, Intersection {A ∩ B}, and Complement { A’ } • Venn Diagrams 6.3 Basic Counting Techniques {Addition and Multiplication Principles} What is probability? In layman’s terms it is the act of assigning numerical value to a particular event. The event might be; winning the lottery, guessing the correct answer on a test question, selecting aan Ace from a deck of cards, having a boy or girl (given that you are pregnant of course), or that a lightbulb will last more than 1000 hours. These are just a few examples of the many applications of probability. How do you determine the probability of an event? To put it simply, you take the number of ways that your event can occur divided by the number of total possibilities. For example, suppose you toss two coins. What is the probability that both coins are heads? There are 4 possible outcomes {(h,h),(h,t),(t,h),(t,t)} and only one way to get the desired event {(h,h)}. Thus, the probability is ¼ . In other examples it might not be so easy to count the total number of possibilities (or the number of ways to get the event). Suppose you buy a lotto ticket and want to know the probability that your numbers will be selected. Could you actually write out all possible scenarios. I doubt it. Or, you are dealt a 5-card hand of cards, and you want to know your chances of getting a full house (3 of one kind and two of another). Would you want to have to write down every 5-card hand that results in a full house, so you could count them? Counting Techniques: Counting techniques give us a way to count how many elements are in a set, without having to actually count them. Caution : During the first couple of sections of this chapter, we will only be determining how many ways an event can occur. We will not be calculating probabilities until section 6.3. I say this because students commonly make the following error my probability test. When a question asks how many possible outcomes there are for an event, students sometimes give the probability for the event. And, when I ask for the probability, students will give the number of possible outcomes. Read the questions carefully. Counting Techniques Discussed in Sections 6.1-6.2 I. Addition Principle II. Multiplication Principle III. Permutations IV. Combinations Before we can talk about how many elements are in a set, we must first learn some set terminology....
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This note was uploaded on 03/27/2008 for the course MATH 1314 taught by Professor Prealg during the Spring '07 term at San Jacinto.

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1324Winter2004Chapter6and7Lecture_Examples - Math 1324...

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