I have an upcoming exam, with 8 questions that may cover 10 fields. Suppose the pass criteria is 70% then how many fields i have to study to clear the exam?
Depends JackSon !
Back then only 70% throughly (as a student)
Now, may be all 100% and use some gimmicks :)
Objectives
Students will: 1.learn what probability is,2.learn different ways to express probability numerically: as a ratio, a decimal, and a percentage, and3.learn how to solve problems based on probability.
Materials
The class will need the following: •Understanding: Probability and Odds video•Copies of Classroom Activity Sheet: Probability Problem Solving•Computers with Internet access (optional but very helpful)•Reference materials such as almanacs and encyclopedias•Copies of Take-Home Activity Sheet: Spin the Wheel!
Procedures
1.Begin the lesson by asking students to define probability (the likelihood or chance that a given event will occur). Probability is usually expressed as a ratio of the number of likely outcomes compared with the total number of outcomes possible. Ask students if they can give an example of probability.2.To help students understand probability, work on the following problem as a class: Imagine that you have boarded an airplane. The rows are numbered from 1 to 30, and there are six seats per row, three on each side of the isle. Seats in each row are labeled A through F. Using that information, work together as a class to solve the problems listed below.
3.To figure out each problem, students must set up a ratio between the total number of outcomes—in these problems either the total number of seats or rows—and the specific question asked. Tell students that they will write their answer as a fraction, decimal, and percentage. Example: The chance of sitting in seat 7A is 1/180, .00555, or .555 percent. The ratio presented as a percentage helps make it clear if the probability of an event is great or small.4.Distribute the Classroom Activity Sheet and tell students that they are going to work on several probability problems in class, expressing the answer as a fraction, decimal, and percentage. Students may work individually or with partners. The problems and the answers are listed below:
5.After students have completed the Classroom Activity Sheet, go over their responses. Then assign the Take-Home Activity Sheet: Spin the Wheel! If time permits, review their answers during the next class period.
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Adaptations
Work on the Classroom Activity Sheet as a whole-class activity. Have students write their answers as a ratio only. Then challenge students to work on the Take-Home Activity Sheet in pairs. Go over their responses in class.
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Discussion Questions
1.Name professions that use probability. Give an example. Many scientists and social scientists use probability, including epidemiologists, psychologists, economists, and statisticians. They predict outcomes of events, such as the incidence of diseases and the strength of the stock market.2.Imagine you are on the school debate team and the subject at hand is whether companies should drill for oil in Antarctica. What statistics would you look for if you're arguing in favor of oil exploration there? What statistics would you look for to support your argument against drilling there? What are some ways that numbers could support arguments on both sides?3.Think about numbers you may have seen in advertisements, such as "X Juice is 90 percent real juice," or "Y cereal has 35 percent of the total vitamins needed in one day." How would you write each percentage as a ratio?4.What does it mean when you hear the weather reporter predict a 10 percent chance of rain? Is that a high or low probability?5.Express the probability that your mother will let you have a sleepover next weekend as a probability, assuming that the total number of outcomes is 100. What factors would increase the probability that she would say yes? (If you finish all your homework and chores, go to bed on time.) What factors would decrease the probability that she would say yes? (If you misbehave, do not finish your homework or chores, or go to bed on time.)6.How do you think authors of The Farmer's Almanac make their predictions about weather for a year? How do you think they use probability?
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Evaluation
Use the following three-point rubric to evaluate students' work during this lesson:
- Three points: demonstrates a strong understanding of probability based on their participation in class, their ability to complete the Classroom Activity Sheet, and their ability to complete the Take-Home Activity Sheet
- Two points: demonstrates a moderate understanding of probability based on their participation in class, their ability to complete the Classroom Activity Sheet, and their ability to complete the Take-Home Activity Sheet
- One point: demonstrates a weak understanding of probability based on their participation in class, their ability to complete the Classroom Activity Sheet, and their ability to complete the Take-Home Activity Sheet.
Extensions
Probability in Advertising
Ask students to look at newspapers and magazines for examples of how numbers are used in advertisements. For example, it is not unusual to see something like "two-thirds less fat than the other leading brand" or "four out of five dentists recommend Brand T gum for their patients who chew gum." Why do advertisers use numbers like these? What information are they trying to convey? Do students think that the numbers give accurate information about a product? Why or why not?
They Said What? Ask students to look at newspapers or magazines for examples of how politicians, educators, environmentalists, or others use data such as statistics and probability. Then have them analyze the use of the information. Why did the person use data? What points were effectively made? Were the data useful? Did the data strengthen the argument? Have students provide evidence to support their ideas. Chance and Average (Math Matters series) Grolier Education, 1999. For a brief but clear presentation of how numbers and chance work together, this volume in the Math Matters series is ideal. Important terms are underlined and included in a short glossary. Clear drawings demonstrate the concepts along with easy experiments to try.
Why Do Buses Come in Threes? The Hidden Mathematics of Everyday Life Rob Eastaway and Jeremy Wyndham. John Wiley & Sons, 1998. Set up in question-and-answer format, this book offers explanations for those questions that perplex us all, starting with "Why can't I find a four-leafed clover?" The text is illustrated with line drawings, and additional problems/questions and solutions appear in shaded boxes. If you need to know "Why am I always in traffic jams?" this is your book
regards
Check this link will help you
Chapter Research on Teaching and Learning Probability
Regards
Thank you for the challenging question. This is about statistics and probabilities. Following.
I also agree with the statement ( go through the whole program ).
The question "How many fields do I have to study to pass the exam?" probably means "How many fields do I have to study to have a given probability of passing the exam?" There are no guaranties about the fields on the exam so only probabilities can be calculated. But this requires information that was not given. Are all fields equally likely to be on the exam? Are all questions in a given field equally likely to be correctly answered? If so, then there is a statistical answer to your question. But my guess is that some fields are more important to the exam giver than others. Your best chance of passing is to study all fields, your next best chance of passing is to study the favorite fields of the exam giver.
My interpretation of "8 questions may cover 10 fields" is that anything is possible. Maybe all 8 questions are from the same field. However, if it is given that each question is in a different field then you should study 8 fields. The worst case is that 2 questions are from the 2 fields you did not study. That makes your score 75%.
Another question that can be answered is the probability of passing the exam when it is given that all fields have the same probability of being represented by a randomly selected question. For example, the questions are randomly selected from a basket containing a very large number of questions with the basket contents prepared so that all 10 fields have equal representation. Let N (an integer from 0 to 10) be the number of fields studied. The probability of a question being from a studied field is N/10. You pass the exam if and only if you give 6 or more correct answers to the 8 questions. The probability of passing the exam, as a function of N, is calculated from the binomial distribution by calculating the probability of 6 or more successes out of 8 tries when the probability of each success is N/10.
I agree with L.D.Edmonds' answer. It can be just like that. Otherwise, if you want to pass, you might refer all the 10 fields or may be at most 9.
The question is not to answer the way it is asked.
Either you ask, how high is the probability in case I study k of n fields, or you ask how many (k) fields do I have to learn to pass with percentage X.
It is a binomial experiment in case the drawing of fields and questions are equally probable and it is a sampling without replacement model (once chosen it can't be drawn again, i.e. not more than one question per topic or equally distributed, i.e. 2,3 etc. questions of each topic or the value of the answers of each field will be equal).
In the question implied is, that each question will be passed once the student learnt the field. In case there is another distribution included, we have a different model.
In this case:
- 10 over 8 possible tuples (45)
- 6 (exactly 5.6) chosen/studied fields are from the winning tuple (8 over 6 = 24 "winning tuples")
- passing probability 53%
==> Studying 6 randomly chosen fields makes passing slightly more probable than failing, which might be enough for average students that aim for leisure time maximization!
- Studying 7 fields elevates the passing probability to 71%.
To be sure to pass the students will have to study all fields, but where is the fun in this!? This separates average students from good students. Real fun starts after a good exam.
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