lec2.1 - 26 Lecture 3: CHAPTER 2: PROBABILITY A chance...

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26 Lecture 3: CHAPTER 2: PROBABILITY A chance experiment , also called a random experiment , is simply an activity or situation whose outcomes, to some degree, depend on chance. To decide whether a given activity qualifies as a chance experiment, ask yourself the question, Will I get exactly the same result if I repeat the experiment more than once? If the answer is “no”, then the experiment qualifies as a chance experiment. Example: Basic Ideas (Section 2.1, page 48) A PROBABILITY is a number between 0 and 1, which measures how likely an event is to occur. The SAMPLE SPACE (S) is the collection of all possible outcomes that can occur in an experiment. The identification of all the possible outcomes in S is often the first step in determining probabilities. An EVENT is a subset of the sample space S. Events are usually denoted by upper case letters (A,B,C,…) and the probability of an event E is denoted by P(E). If all the outcomes in the experiment are “equally likely”, then the probability of an event is given by: P(Event) = # of outcomes in the event / # of outcomes in S
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27 Example: A “fair” die is tossed. List the sample space S and the probability of rolling a 4. In many experiments we can use a “tree diagram” to list the possible outcomes of the experiment (i.e. the Sample Space S) and the probabilities of each outcome. Example: A fair four sided die is rolled twice. (a) Use a tree diagram to list the sample space S. (b) List and find the probability of each of the following events. A = “a sum of 4 or less” B = “the second roll is a 2”
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28 Combining Events and Probabilities Another visual device, the Venn Diagram , is especially useful for depicting relationships between events. This is what a possible Venn diagram looks like: Shaded areas of the Venn diagram represent probabilities of certain events. I’ll explain this further in a minute, but first: Definition: Example: For the above example, we listed the sample space of rolling a fair four sided die and listed the probability
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lec2.1 - 26 Lecture 3: CHAPTER 2: PROBABILITY A chance...

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