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MDM 4U Unit 3: Probability Review and Preview of Probability Assignment Due Wednesday, October 3, 3012 Name: ______________________ The following assignment is to be started in class following the Unit 2 test and completed for homework. Assignments are to be your own work! Any assignments handed in which are the same form, set up, errors, etc. (I.e. simply copied from someone else) will not be evaluated. 1. Review of Prerequisite Skills: Probability involves being able to count the number of ways an event can occur or the total number of possible outcomes to an experiment. To prepare for this unit you will review some counting theory. Complete the following showing full and justified solutions. Page 302 # 6, 7, 8, 9, 10, 13, 14, 16, 17 2. **Check your answers in back of text! Explain the meaning of each of the following terms and give an example. Read pages 304 – 307 and use the Glossary at the back of the text to help. a) Probability b) Probability Experiment c) Trials d) Outcomes e) Sample Space, S f) Events g) Probability of an Event and what value it can have. h) Empirical Probability i) Theoretical Probability and how to calculate it. Review and Preview of Probability Assignment Due Wednesday, October 3, 3012 MDM 4U Category Knowledge/ Understanding Communication Application Name: ______________________ Level 4 Level 3 Level 2 Level 1 Below Level 1 Demonstrates a solid and thorough understanding of counting principles and probability terminology. Demonstrates good understanding of counting principles and probability terminology. Demonstrates moderate understanding of counting principles and probability terminology Demonstrates a limited or inaccurate understanding of counting principles and probability terminology Demonstrates insufficient understanding of counting principles and probability terminology Provides a thorough, clear and insightful explanation/justification (solutions are well formed, with completeness, accuracy and full proper mathematical form) Provides a complete, clear, and logical explanation, missing small details (solutions are complete but some proper form is missing –i.e. therefore statements) Provides a partial explanation/justification that shows some clarity and logical thought (solutions are somewhat complete, but disorganized) Provides a limited or inaccurate explanation/justification that lacks clarity or logical thought (solutions are incomplete, scattered and disorganized) Demonstrates insufficient understanding of proper mathematics form for solutions (solutions are minimal and incomplete, no math form show) Assignment is complete, handed in on time and completely demonstrates the individual student’s thinking. Assignment is complete, handed in on time and most work demonstrates the individual student’s thinking. Assignment is complete, handed in on the due date and some of the work demonstrates the individual student’s thinking while some shows input from others. Assignment is almost complete, handed in on the due date and demonstrates little of the individual student’s thinking while most shows input from others. Assignment has little work complete and/or was not handed in on the due date and/or is a copy of someone else’s work. Confidently and accurately applies probability and counting concepts to solve problems with no error. Confidently applies probability and counting concepts to solve problems with little error. Somewhat applies probability and counting concepts to answer questions. Applies limited probability and counting concepts to answer questions. Insufficient probability and counting concepts applied to answer questions. Review and Preview of Probability Assignment Due Wednesday, October 3, 3012 Solutions 1. Review of Prerequisite Skills: Probability involves being able to count the number of ways an event can occur or the total number of possible outcomes to an experiment. To prepare or this unit you will review some counting theory. Complete the following showing full and justified solutions. Page 302 # 6, 7, 8, 9, 10, 13, 14, 16, 17 **Check your answers in back of text! 2. Explain the meaning of each of the following terms and give an example. Read pages 304 – 307 and use the Glossary at the back of the text to help. a) Probability: is the branch of mathematics that deals with chance, random variables, and the likelihood of outcomes. Ex. The probability of rain is 60% today. b) Probability Experiment: a well defined process consisting of a number of trials in which clearly distinguishable outcomes are observed. Ex. Flip a coin 10 times and record whether you flip heads or tails. c) Trials: A step in a probability experiment in which an outcome is produced and tallied. Ex. From b) each flip of the coin is a trial. d) Outcomes: possible results of an experiment or action. Ex. The outcome of the coin flipping experiment would be how many head or tails and in what order they happened. HHHTTHTTTH is one possible outcome. e) Sample Space, S: The set of all possible outcomes in a probability experiment. Ex. The sample space for the coin flipping experiment would be the set of all the different ways the 10 trials could have turned out. f) Event: A group of outcomes to an experiment with specified characteristics. Ex. Event A could be the set of outcomes where there were 3 Heads and 7 Tails. g) Probability of an Event and what value it can have: P(A), is a quantified measure of the likelihood that the event will occur. The probability of an event is always a value between 0 and 1. Ex. When you flip a coin the probability of getting Tails is 0.5 h) Empirical Probability: (also called experimental or relative frequency probability) is determined by dividing the number of times that the event actually occurs in an experiment by the number of trials. Ex. If you found that 3 of the ten trials had 3 Heads and 7 Tails, then the Emperical 3 Probability of getting 3 heads in 10 flips if 10 . i) Theoretical Probability and how to calculate it: is deduced from analysis of the possible outcomes. For example if all outcomes are equally likely then P(A) = n(A) n(S)