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 A simulation imitates a real situation  Is supposed to give similar results  And so acts as a predictor of what should actually happen  It is a model.

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Presentation on theme: " A simulation imitates a real situation  Is supposed to give similar results  And so acts as a predictor of what should actually happen  It is a model."— Presentation transcript:

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2  A simulation imitates a real situation  Is supposed to give similar results  And so acts as a predictor of what should actually happen  It is a model in which repeated experiments are carried out for the purpose of estimating in real life

3  Used to solve problems using experiments when it is difficult to calculate theoretically  Often involves either the calculation of: ◦ The long-run relative frequency of an event happening ◦ The average number of ‘visits’ taken to a ‘full-set’  Often have to make assumptions about situations being simulated. E.g. there is an equal chance of producing a boy or a girl

4  Maths online Maths online

5  AC/on  RUN  OPTN  F6  PROB  Ran#

6 1. To Simulate tossing of a coin ◦ Ran#  Heads:  Tails: – To simulate LOTTO balls ◦ 1+40Ran#, truncate the result to 0 d.p., or ◦ Ran#, truncate the result to 0 d.p.

7 3. To simulate an event which has 14% chance of success ◦ 100Ran#, truncate the result to 0 d.p.  0 – 13 for success, for failure, or ◦ 1+100Ran#, truncate the result to 0 d.p.  1-14 for success, for failure

8  Assume each day has equal probability (1/7)  Use spreadsheet function RANDBETWEEN(1,7)  Generate 4 random numbers to simulate one family  Repeat large number of times Day of the week Random Number Sunday1 Monday2 Tuesday3 Wednesda y 4 Thursday5 Friday6 Saturday7

9 The description of a simulation should contain at least the following four aspects: Tools  Definition of the probability tool, eg. Ran#, Coin, deck of cards, spinner  Statement of how the tool models the situation Trials  Definition of a trial  Definition of a successful outcome of the trial Results  Statement of how the results will be tabulated giving an example of a successful outcome and an unsuccessful outcome  Statements of how many trials should be carried out

10 Calculations Statement of how the calculation needed for the conclusion will be done Long-run relative frequency = Mean =

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12 Tool: First digit using calculator 1+10Ran# Odd Numbers stands for ‘Boy’ and Even Number stands for ‘Girl’ Trial:One trial will consist of generating 4 random numbers to simulate one family. A Successful trial will have 2 odd and 2 even numbers. Results: Number of Trials needed: 30 would be sufficient Calculation: Probability of 2 boys & 2 girls = TrialOutcome of trial Result of trial 12357Unsuccessful 24635Successful

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14 Tool: Generate random numbers between 1 & 6 (inclusive), each number stands for each toy. Trial: One trial will consist of generating random numbers till all numbers from 1 to 6 have been generated. Count the number of random numbers need to get one full set Results : Number of Trials needed: 30 would be sufficient Calculation : Average number of visits = Total visits Number of trials TrialToy 1 Toy 2 Toy 3 Toy 4 Toy5Toy6TallyTotal Visits 1YYYYYY10 2YYYYYY19

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16 Tool: The probability that Mary guesses a question true is one half. First digit using calculator Ran# 1to 5stands for ‘correct answer’ 6 to 10stands for ‘incorrect answer’ Trial:One trial will consist of generating 3 random numbers to simulate Mary answering one complete test. A successful outcome will be getting atleast 2 of the 3 random numbers between 1 and 5. Results : Number of Trials needed: 30 would be sufficient Calculation: Estimate of probability of ‘passing’ the exam = TrialOutcome of TrialResult of Trial 1122Successful trial 2167Unsuccessful trial

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18 Tool: The probability that Mary guesses a question true is one half. First digit using calculator Ran# 1to 5stands for ‘correct answer’ 6 to 10stands for ‘incorrect answer’ Trial:One trial will consist of generating 8 random numbers to simulate Mary answering one complete test. A successful outcome will be getting atleast 4 of the 8 random numbers between 1 and 5. Results: Number of Trials needed: 30 would be sufficient Calculation: Estimate of probability of ‘passing’ the exam = TrialOutcome of TrialResult of Trial Successful trial Unsuccessful trial

19 Problem: Lotto 40 balls and to win you must select 6 in any order. In this mini Lotto, there are only 6 balls and you win when you select 2 numbers out of the 6. Design and run your own simulation to estimate the probability of winning (i.e. selecting 2 numbers out of the 6) Calculate the theoretical probability of winning.

20 Tool: Two numbers (between 1 and 6) will need to be selected first (say 2 & 4) First digit using calculator 1 + 6Ran#, ignore the decimals. Trial:One trial will consist of generating 2 random numbers Discard any repeat numbers A successful outcome will be getting 2 of the 6 random numbers generated Results : Number of Trials needed: 50 would be sufficient Calculation: Estimate of probability of ‘winning’ = Number of ‘successful’ outcome Number of trials Theoretical probability in this case is 1/15 TrialOutcome of TrialResult of Trial 12 4Successful trial 213Unsuccessful trial


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