Geometric Probability I

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bulletObjective:  Students will be able to:
bulletCalculate the expected value of a probability based-game
bulletUse the concepts and formulas to calculate area to calculate geometric probability
bulletModel situations involving probability with simulations and solve problems using these models

 

bulletResources
bullet Geometric Probability Activity Sheets
bulletpaper clips
bullet homework sheets
bullet transparencies for each situation being studied by students

 

bulletLesson Plan
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Roll one dice and ask students what the probability of rolling a 6 is?

Ask students what they must know to determine probability of rolling a 6?

Bring out definition of probability of an event:

 

bulletDistribute the activity sheet and highlight the three problems we will be discussing today.  Challenge students to think about how the concept of probability can be applied to each problem.
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Distribute paper clips and demonstrate how to spin the paper clip.  Have each pair of students spin the spinner 36 times and record their results in a table.    Collect the data on the number of times the spinner lands in each of the regions.  Determine the probability of spinning A, B, C, or D from the data. 
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Is there another way we could determine the probability of spinning A, B, C, or D?

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What do we need to know to find the probability for the spinner?

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180, 90, 60, 30 degrees, portion of circle that each angle is, total number of degrees in the circle, area of the sector of the circle

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Have students calculate the probability of landing in each sector.

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Ask:  What is the probability that you will spend the evening with your younger brother?  What is the probability you will play in a band?  What is the probability that you will not spend the evening with your younger brother?

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This is geometric probability since it is based upon a geometric figure. 

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Guide students in finding the probability of selecting the shortest diagonal in a regular hexagon.  Discuss solution to problem.  Relate to definition of probability.

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Guide students to solve Jose’s graphing probability question.  Assist students in determining which points satisfy the given condition.  Help Jose find this probability.  Relate probability to the area of the regions involved

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Guide students to solve the bus stop problem  Students will use the picture to find the probability.

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Guide the students to solve the ping pong ball board problem

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Summarize how the definition of probability

was used in each situation.  Summarize how geometric properties on each problem helped to find the values for the numerator and denominator of this definition.
 

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Four problems on a homework sheet to assess if students understood the various geometric probability problems solved in class.

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Monitor student activity to see that they are making the connection between their former understanding of probability and its application to the geometric figures involved in each question.