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| The | | The |
− | words '''‘probably’, | + | words '''‘probably’,''' |
− | ‘doubt’, ‘most probably’, ‘chances’''', | + | ‘doubt’, ‘most probably’, ‘chances’''',''' |
| etc., used in the statements above involve an element of uncertainty. | | etc., used in the statements above involve an element of uncertainty. |
| For example, in (1), ‘probably rain’ will mean it may rain or may | | For example, in (1), ‘probably rain’ will mean it may rain or may |
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| on blue is one fourth. | | on blue is one fourth. |
| | | |
− | '''Impossible | + | '''Impossible''' |
− | Event '''is | + | Event '''is''' |
| an event that can never occur. The probability of landing on purple | | an event that can never occur. The probability of landing on purple |
| after spinning the spinner is impossible as it is | | after spinning the spinner is impossible as it is |
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| colour. | | colour. |
| | | |
− | '''Certain | + | '''Certain''' |
− | events:''' | + | events: |
| That the event will surely occur. If we consider the situation where | | That the event will surely occur. If we consider the situation where |
| A | | A |
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| particular trial is an '''event''' with a particular outcome head. | | particular trial is an '''event''' with a particular outcome head. |
| | | |
− | Now if we say let n be the number of trials, then the '''experimental | + | Now if we say let n be the number of trials, then the '''experimental''' |
− | probability P(E)''' of an event E happening is given by | + | probability P(E)''' of an event E happening is given by''' |
| | | |
| [[Image:KOER%20Probability,%20Permutations%20and%20Combinations_html_68e91ef4.gif]] | | [[Image:KOER%20Probability,%20Permutations%20and%20Combinations_html_68e91ef4.gif]] |
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| where 0 means it is impossible for the event to occur and 1 means its certain to occur. | | where 0 means it is impossible for the event to occur and 1 means its certain to occur. |
| The | | The |
− | '''theoretical | + | '''theoretical''' |
− | probability'''
| + | probability |
| (also called classical probability) of an event E, written as P(E), | | (also called classical probability) of an event E, written as P(E), |
− | where we assume that the outcome of the events are ''equally | + | where we assume that the outcome of the events are ''equally'' |
− | likely'' | + | likely |
| | | |
| [[Image:KOER%20Probability,%20Permutations%20and%20Combinations_html_48cf88f6.gif]] | | [[Image:KOER%20Probability,%20Permutations%20and%20Combinations_html_48cf88f6.gif]] |
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| example, to find the experimental probability of winning a game, one | | example, to find the experimental probability of winning a game, one |
| must play the game many times, then divide the number of games won by | | must play the game many times, then divide the number of games won by |
− | the total number of games played '''P''''''robability''' | + | the total number of games played '<nowiki/>''P'<nowiki/>'''''robability''' |
| | | |
| The measure of how likely it is for an event to | | The measure of how likely it is for an event to |
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| = Teaching Outlines = | | = Teaching Outlines = |
| | | |
− | ==Concept #1 Introduction to Probability== | + | ==Concept - 1 Experimental Probability== |
| | | |
| + | === Learning objectives === |
| + | Perform a random experiment and tabulate results and calculate the experimental probability of some events. |
| | | |
| + | === Notes for teachers === |
| | | |
− | ===Learning objectives=== | + | === Activities === |
| + | # Activity No 1: [[Experimental Probability Activity 1|Experimental_Probability_Activity1]] |
| + | # Activity No 2: [[Even and Odd Probability Activity2]] |
| + | |
| + | == Concept - 2 Introduction to Probability == |
| + | |
| + | === Learning objectives === |
| #Understand that events occur with different frequencies | | #Understand that events occur with different frequencies |
| #Different events have different likelihoods (likely, unlikely, equally likely, not equally likely) | | #Different events have different likelihoods (likely, unlikely, equally likely, not equally likely) |
| #Understand the idea of sample space and universe of events | | #Understand the idea of sample space and universe of events |
− |
| |
− |
| |
| | | |
| ===Notes for teachers=== | | ===Notes for teachers=== |
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| #Compare the results across groups. | | #Compare the results across groups. |
| #To develop an understanding of what chance means? | | #To develop an understanding of what chance means? |
− |
| |
− |
| |
| ===Activities=== | | ===Activities=== |
| #Activity No #1 '''[[probability_introduction_activity1]]''' | | #Activity No #1 '''[[probability_introduction_activity1]]''' |
| #Activity No #2 '''[[probability_introduction_activity2]]''' | | #Activity No #2 '''[[probability_introduction_activity2]]''' |
− |
| |
− |
| |
| | | |
| ==Concept #2 Different types of events== | | ==Concept #2 Different types of events== |
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| ===Notes for teachers=== | | ===Notes for teachers=== |
− |
| |
− |
| |
| | | |
| ===Activities=== | | ===Activities=== |
| #Activity No #1 '''[[probability_types_of_events_activity1]]''' | | #Activity No #1 '''[[probability_types_of_events_activity1]]''' |
− | #Activity No #2 '''[[probability_types_of_events_activity2]]''' | + | #Activity No #2 |
| | | |
| ==Concept #3 Conditional probability== | | ==Concept #3 Conditional probability== |
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| #Activity No #2 '''Concept Name - Activity No.''' | | #Activity No #2 '''Concept Name - Activity No.''' |
| | | |
− | | + | == Further Explorations == |
| + | #Math Probability - What a Fun Unit!, http://www.algebra-class.com/math-probability.html |
| + | #Khan Academy Probability Part1, [] |
| + | #Khan Academy Probability Part1, [] |
| + | #Lecture - 1 Introduction to the Theory of Probability, http://www.youtube.com/watch?v=r1sLCDA-kNY&feature=related |
| =Assessment activities for CCE= | | =Assessment activities for CCE= |
| | | |