Difference between revisions of "Probability"
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While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist''']. | While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist''']. | ||
| + | = Concept Map = | ||
| + | [[File:probability.mm|Flash]] | ||
| + | |||
| + | __FORCETOC__ | ||
= Introduction = | = Introduction = | ||
A brief history of how probability was developed | A brief history of how probability was developed | ||
| Line 30: | Line 34: | ||
probability b) Theoretical approach to probability. The basic | probability b) Theoretical approach to probability. The basic | ||
principle of counting is covered. | principle of counting is covered. | ||
| + | |||
| + | In everyday life, we come across statements such as | ||
| + | 1. It will probably rain today. | ||
| + | 2. I doubt that he will pass the test. | ||
| + | 3. Most probably, Kavita will stand first in the annual examination. | ||
| + | 4. Chances are high that the prices of diesel will go up. | ||
| + | 5. There is a 50-50 chance of India winning a toss in today’s match. | ||
| + | |||
| + | The | ||
| + | words '''‘probably’, | ||
| + | ‘doubt’, ‘most probably’, ‘chances’''', | ||
| + | etc., used in the statements above involve an element of uncertainty. | ||
| + | For example, in (1), ‘probably rain’ will mean it may rain or may | ||
| + | not rain today. We are predicting rain today based on our past | ||
| + | experience when it rained under similar conditions. Similar | ||
| + | predictions are also made in other cases listed in (2) to (5). | ||
| + | |||
| + | The uncertainty of ‘probably’ etc. can be measured numerically by | ||
| + | means of ‘probability’ in many cases. Though probability started | ||
| + | with gambling, it has been used extensively in the fields of Physical | ||
| + | Sciences, Commerce, Biological Sciences, Medical Sciences, WeatherForecasting,etc. | ||
| + | |||
| + | Probability theory like many other branches of mathematics, evolved out of | ||
| + | practical consideration. It had its origin in the 16th century when | ||
| + | an Italian physician and mathematician Jerome Cardan (1501–1576) | ||
| + | wrote the first book on the subject “Book on Games of Chance” | ||
| + | (Biber de Ludo Aleae). It was published in 1663 after his death. | ||
| − | + | When something occurs it is called an '''event'''. | |
| − | + | For example : A spinner has 4 equal sectors coloured | |
| + | yellow, blue, green and red. What are the chances of landing on blue | ||
| + | after spinning the spinner? What are the chances of landing on red? | ||
| + | The chances of landing on blue are 1 in 4, or one fourth. The chances | ||
| + | of landing on red are 1 in 4, or one fourth. | ||
| + | |||
| + | An | ||
| + | '''experiment''' | ||
| + | is a situation involving chance or probability that leads to results | ||
| + | called outcomes. In the problem above, the experiment is spinning the | ||
| + | spinner. | ||
| + | |||
| + | An | ||
| + | '''outcome''' | ||
| + | is the result of a single trial of an experiment. The possible | ||
| + | outcomes are landing on yellow, blue, green or red. | ||
| + | |||
| + | An | ||
| + | '''event''' | ||
| + | is one or more outcomes of an experiment. One event of this | ||
| + | experiment is landing on blue. | ||
| + | |||
| + | '''Probability''' | ||
| + | is the measure of how likely an event is. The probability of landing | ||
| + | on blue is one fourth. | ||
| + | |||
| + | '''Impossible | ||
| + | Event '''is | ||
| + | an event that can never occur. The probability of landing on purple | ||
| + | after spinning the spinner is impossible as it is | ||
| + | impossible to land on purple since the spinner does not contain this | ||
| + | colour. | ||
| − | + | '''Certain | |
| + | events:''' | ||
| + | That the event will surely occur. If we consider the situation where | ||
| + | A | ||
| + | teacher chooses a student at random from a class of 30 girls. What is | ||
| + | the probability that the student chosen is a girl? Since all the | ||
| + | students in the class are girls, the teacher is certain to choose a | ||
| + | girl. | ||
= Textbook = | = Textbook = | ||
Revision as of 12:10, 29 January 2020
| Philosophy of Mathematics |
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Concept Map
Introduction
A brief history of how probability was developed within the discipline of mathematics. Random processes can be modelled or explained mathematically by using a probability model. The two probability models are a) Experimental approach to probability b) Theoretical approach to probability. The basic principle of counting is covered.
In everyday life, we come across statements such as
1. It will probably rain today. 2. I doubt that he will pass the test. 3. Most probably, Kavita will stand first in the annual examination. 4. Chances are high that the prices of diesel will go up. 5. There is a 50-50 chance of India winning a toss in today’s match.
The words ‘probably’, ‘doubt’, ‘most probably’, ‘chances’, etc., used in the statements above involve an element of uncertainty. For example, in (1), ‘probably rain’ will mean it may rain or may not rain today. We are predicting rain today based on our past experience when it rained under similar conditions. Similar predictions are also made in other cases listed in (2) to (5).
The uncertainty of ‘probably’ etc. can be measured numerically by means of ‘probability’ in many cases. Though probability started with gambling, it has been used extensively in the fields of Physical Sciences, Commerce, Biological Sciences, Medical Sciences, WeatherForecasting,etc.
Probability theory like many other branches of mathematics, evolved out of practical consideration. It had its origin in the 16th century when an Italian physician and mathematician Jerome Cardan (1501–1576) wrote the first book on the subject “Book on Games of Chance” (Biber de Ludo Aleae). It was published in 1663 after his death.
When something occurs it is called an event. For example : A spinner has 4 equal sectors coloured yellow, blue, green and red. What are the chances of landing on blue after spinning the spinner? What are the chances of landing on red? The chances of landing on blue are 1 in 4, or one fourth. The chances of landing on red are 1 in 4, or one fourth.
An experiment is a situation involving chance or probability that leads to results called outcomes. In the problem above, the experiment is spinning the spinner.
An outcome is the result of a single trial of an experiment. The possible outcomes are landing on yellow, blue, green or red.
An event is one or more outcomes of an experiment. One event of this experiment is landing on blue.
Probability is the measure of how likely an event is. The probability of landing on blue is one fourth.
Impossible Event is an event that can never occur. The probability of landing on purple after spinning the spinner is impossible as it is impossible to land on purple since the spinner does not contain this colour.
Certain events: That the event will surely occur. If we consider the situation where A teacher chooses a student at random from a class of 30 girls. What is the probability that the student chosen is a girl? Since all the students in the class are girls, the teacher is certain to choose a girl.
Textbook
Please click here for Karnataka and other text books.
Karnataka text book for Class 10, Chapter 05-Probability
Additional Information
Useful websites
- To get the information about probability click here
Lessons and activities:
http://www-tc.pbs.org/teachers/mathline/lessonplans/pdf/esmp/chancesare.pdf http://www.bbc.co.uk/schools/teachers/ks2_lessonplans/maths/probability.shtml
Activities on Probability:
http://www.cimt.plymouth.ac.uk/projects/mepres/allgcse/as5act1.pdf
How to teach probability
http://nrich.maths.org/probability http://nrich.maths.org/9853
Possible video resource for dubbing
Reference Books
- http://www.teachingideas.co.uk/maths/probabilitycards.htm
- http://www.teachingideas.co.uk/maths/files/probabilitycards.pdf
Teaching Outlines
Concept #1 Introduction to Probability
Learning objectives
- Understand that events occur with different frequencies
- Different events have different likelihoods (likely, unlikely, equally likely, not equally likely)
- Understand the idea of sample space and universe of events
Notes for teachers
- To understand likelihood of events happening
- The objective here is not numerical computation but to understand events, likelihoods and vocabulary of description. The activity can be done in groups/ pairs. Not a whole class activity.
- Compare the results across groups.
- To develop an understanding of what chance means?
Activities
- Activity No #1 probability_introduction_activity1
- Activity No #2 probability_introduction_activity2
Concept #2 Different types of events
Learning objectives
- Understand elementary and compound events and construction of such events
- Complementary events
- Independent events / Mutually exclusive events
Notes for teachers
Activities
- Activity No #1 probability_types_of_events_activity1
- Activity No #2 probability_types_of_events_activity2
Concept #3 Conditional probability
Learning objectives
Notes for teachers
Activities
- Activity No #1 Concept Name - Activity No.
- Activity No #2 Concept Name - Activity No.