No notes for slide. Teaching Suggestion 2. Students need to understand where probabilities come from. Sometimes they are subjective and based on personal experiences. Other times they are objectively based on logical observations such as the roll of a die. Often, probabilities are derived from historical data—if we can assume the future will be about the same as the past.
This concept is often foggy to even the best of students—even if they just completed a course in statistics. Use practical examples and drills to force the point home. The table at the end of Example 3 is especially useful. Students must understand why we subtract P A and B.
Explain that the intersect has been counted twice. Figure 2. This example works well to explain conditional probability of dependent events. An even better idea is to bring 10 golf balls to class. Six should be white and 4 orange yellow. Mark a big letter or number on each to correspond to Figure 2.
You can also use the props to stress how random sampling expects previous draws to be replaced. Students often have problems understanding the concept of random variables. Instructors need to take this abstract idea and provide several examples to drive home the point.
Table 2. A probability distribution is often described by its mean and variance. These important terms should be discussed with such practical examples as heights or weights of students. But students need to be reminded that even if most of the men in class or the United States have heights between 5 feet 6 inches and 6 feet 2 inches, there is still some small probability of outliers.
Stress how important the normal distribution is to a large number of processes in our lives for example, filling boxes of cereal with 32 ounces of cornflakes. Each normal distribution depends on the mean and standard deviation. Discuss Figures 2. The IQ example in Figure 2. Students are typically curious about the chances of reaching certain scores. The symmetry requires special care. It never sold fewer than 8 nor more than Assuming that the past is similar to the future, here are the probabilities: Sales No.
Days Probability 8 10 0. Outcome Probability A 0. Alternative Example 2. Ten are female F and U. A name is randomly selected from the class roster and it is female. What is the probability that the student is a U. Not U. Each class has 24 students, and on the surface, both classes appear identical. One class, however, consists of students who have all taken calculus in high school.
The instructor has no idea which class is which. A section is selected at random and quizzed. More than half the class received As. Now, what is the revised probability that the class was the advanced one? The number of students responding to each possibility is shown below: Number of games Number of students 5 40 4 30 3 20 2 10 1 0 A probability distribution of the results would be: Number of games Probability P X 5 0.
Probabilities are shown in graph form below. Find the probability that a rod selected randomly will have a length a. There are two basic laws of probability. First, the probability of any event or state of nature occurring must be greater than or equal to zero and less than or equal to 1.
Second, the sum of the simple probabilities for all possible outcomes of the activity must equal 1. Events are mutually exclusive if only one of the events can occur on any one trial. Events are collectively exhaustive if the list of outcomes includes every possible outcome. An example of mutually exclusive events can be seen in flipping a coin. The outcome of any one trial can either be a head or a tail. Thus, the events of getting a head and a tail are mutually exclusive because only one of these events can occur on any one trial.
This assumes, of course, that the coin does not land on its edge. The outcome of rolling the die is an example of events that are collectively exhaustive. In rolling a standard die, the outcome can be either 1, 2, 3, 4, 5, or 6. These six outcomes are collectively exhaustive because they include all possible outcomes. To learn more, view our Privacy Policy. To browse Academia. Log in with Facebook Log in with Google.
Remember me on this computer. Enter the email address you signed up with and we'll email you a reset link. Need an account? Click here to sign up. Download Free PDF. If you are a university student, you can find extensive selection of textbook, paper, report, etc. Intended for product buyers, you may surf for a complete product instruction manual and guidebook and thus download all of them absolutely free.
This listing are filled with by far the most related and relevant subject identical to your current term and even organize into a compact list for your comfort by our program. We hope you can get something useful by offering you even more alternatives.
0コメント