DESCRIBING SIMULATIONS 20/11/2018 S. Berg

MEAN = Sum of trial results T T R C Tool: - Definition of the probability tool - Statement of how the tool models the situation Trial: - 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 - Statement of how many trials should be carried out Calculation: - Statement of how the calculation needed for the conclusion will be done MEAN = Sum of trial results Number of trials 20/11/2018

TRUE - FALSE TEST PROBLEM Paul has not studied for his history test. He does not know any of the answers on an eight question true-false test, and he decides to guess on all eight questions. Design a simulation to estimate the probability that Paul will “Pass” the test. (ie. Guess the correct answers to four or more of the eight questions) 20/11/2018

Soln - True - False test problem CALCULATOR (10 Ran# +1) (RAN# =OPTN / F6 / F3 / F4 / F1) 1 to 5 = Correct Answer 6 to 10 = Wrong Answer Tool: Trial: - One trial = generating 8 random numbers A successful outcome is gaining 4 OR MORE numbers from 1 to 5 inclusive 20/11/2018 MEAN = Sum of trial results Number of trials

PROB OF PASS= Nos successful trials Results: Trial Outcome Result 1 1,5,8,7,9,6,2,7 X 2 7,4,9,2,3,1,6,5 √ - Repeat for 30 trials Calculation: PROB OF PASS= Nos successful trials 30 20/11/2018

MINIBUS PROBLEM Bob drives a minibus that has 8 seats People buy tickets in advance, but on average, 30% of those who buy tickets do not show up. So Bob has decided to pre-sell ten tickets for each trip. Sometimes more than eight people show up with tickets and Bob is obviously embarrassed. Design a simulation to estimate the probability that Bob will be embarrassed. 20/11/2018

MEAN = Sum of trial results Soln - MINIBUS PROBLEM CALCULATOR (10 Ran# +1) 1 to 3 = Passenger doen’t show up 4 to 10 = Passenger shows up Tool: Trial: - One trial = generating 10 random numbers Bob will be embarrassed if there are MORE THAN 8 numbers from 4 to 10 inclusive 20/11/2018 MEAN = Sum of trial results Number of trials

PROB OF EMBARRASSEMNENT = Nos successful trials Results: Trial Outcome Result 1 4,5,8,7,9,6,2,7,10,9 Embarrassed 2 7,4,9,2,3,2,6,5,8,7 Not - Repeat for 30 trials Calculation: PROB OF EMBARRASSEMNENT = Nos successful trials 30 20/11/2018

CEREAL CARDS A cereal manufacturer includes a gift coupon in each box of its best selling brand. The coupons can be exchanged for a gift when a complete set of 6 coupons have been collected. Design a simulation to calculate the EXPECTED NUMBER of cereal boxes you would have to buy to obtain a complete set of six coupons. 20/11/2018

MEAN = Sum of trial results Soln - CEREAL CARDS CALCULATOR (6 Ran# +1) 1 to 6 = Each of the 6 different cards Tool: Trial: - One trial = generating random numbers until you have at least one of each number 20/11/2018 MEAN = Sum of trial results Number of trials

E(Boxes of Cereal)= Sum of Results Column Trial Outcome Result 1 1,5,3,6,4,5,4,2 8 2 6,5,3,5,4,6,1,3,2 9 - Repeat for 30 trials Calculation: E(Boxes of Cereal)= Sum of Results Column 30 20/11/2018

Copy and complete the table for the relative frequency of flipping a coin 50 times Flip Number Head/Tail Relative Frequency 1 H 2 T 1/2 50 20/11/2018

GRAPH YOUR RESULTS Compare your results with the first graph you drew. What do you notice? 20/11/2018