chp3 - 1 Chapter 3 Probability 3.1 Terminology 3.2 Assign...

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Unformatted text preview: 1 Chapter 3 Probability 3.1 Terminology 3.2 Assign Probability 3.3 Compound Events 3.4 Conditional Probability 3.5 Rules of Computing Probabilities 3.6 Random Sampling Homework:3, 7, 17, 23, 27, 29, 32, 35, 37, 43, 50, 55, 57, 61 2 Section 3.1: Some terminology of probabilities We discussed how to understand/describe the information contained in a sample in Chapter II. However, we want to make inference based on the information contained in a sample as well. We will discuss the concept of probability in this chapter because probability plays an important role in inference making process. Let start our discussion with one example. 3 <Example 3.1>: (Basic) Suppose there is a bag of M&M chocolate with six different coating colors -- 300 brown, 250 red, 200 yellow, 150 orange, 100 green, and 100 tan. Suppose one piece is drawn at random and the coating color is recorded. (a) Is this a random experiment ? (b) How many sample points in this random experiment? (c) What is the sample space of this random experiment? (d) What is the probability of drawing a yellow M&M chocolate? (e) What is the event of drawing a piece of M&M with your favorite colors if your favorite colors are yellow and green? 4 Section 3.2: Assign probability to a sample point and to an event There are two approaches, the relative frequency approach and subjective approach, to assign a probability to a sample point. Both approaches need to follow two basic rules. The first rule is that the probability for each sample point must lie between 0 and 1 . The second rule is that the probabilities of all the sample points within a sample space must sum to 1 . We use the subjective approach to assign probability in Example 3.2 and 3.4 because the frequency tables are unavailable, and use the relative frequency approach to assign probability in Example 3.1 and 3.3 because the frequency tables are available. Usually, we use relative frequency approach to assign probability if the frequency table is available. 5 We can employ the following five steps to compute the probability of an event. (1) Define the experiment. (2) List all the sample points. (3) Assign probability to each sample point. (4) Find out all the sample points in this event. (5). Sum the probabilities of these sample points. 6 <Example 3.2>: (Basic) Two fair coins are randomly tossed, and their up faces are recorded. (a) Is this a random experiment? (b) Write down the sample space. (c) Assign probabilities to each sample points. (d) Event A is at least one head. Event B is at least one tail. Compute the probability of event A and event B. 7 <Example 3.3>: (Basic) Suppose that we repeat toss a pair of fair coins ten thousand times. Table 3.1 is the frequency table of this random experiment....
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chp3 - 1 Chapter 3 Probability 3.1 Terminology 3.2 Assign...

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