08/08/20151 S. Berg DESCRIBING SIMULATIONS

08/08/20152 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

08/08/20153 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)

08/08/20154 Soln - True - False test problem Tool: -CALCULATOR (10 Ran# +1) -(RAN# =OPTN / F6 / F3 / F4 / F1) 1 to 5 = Correct Answer 6 to 10 = Wrong Answer Trial: - One trial = generating 8 random numbers - A successful outcome is gaining 4 OR MORE numbers from 1 to 5 inclusive MEAN = Sum of trial results Number of trials

08/08/20155 Results: - Repeat for 30 trials Calculation: PROB OF PASS= Nos successful trials 30 TrialOutcomeResult 11,5,8,7,9,6,2,7X 27,4,9,2,3,1,6,5√

08/08/20156 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.

08/08/20157 Soln - MINIBUS PROBLEM Tool: -CALCULATOR (10 Ran# +1) 1 to 3 = Passenger doen’t show up 4 to 10 = Passenger shows up Trial: - One trial = generating 10 random numbers - Bob will be embarrassed if there are MORE THAN 8 numbers from 4 to 10 inclusive MEAN = Sum of trial results Number of trials

08/08/20158 Results: - Repeat for 30 trials Calculation: PROB OF EMBARRASSEMNENT = Nos successful trials 30 TrialOutcomeResult 14,5,8,7,9,6,2,7,10,9 Embarrassed 27,4,9,2,3,2,6,5,8,7 Not Embarrassed

08/08/20159 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.

08/08/ Soln - CEREAL CARDS Tool: -CALCULATOR (6 Ran# +1) 1 to 6 = Each of the 6 different cards Trial: - One trial = generating random numbers until you have at least one of each number MEAN = Sum of trial results Number of trials

08/08/ Results: - Repeat for 30 trials Calculation: E(Boxes of Cereal)= Sum of Results Column 30 TrialOutcomeResult 11,5,3,6,4,5,4,28 26,5,3,5,4,6,1,3,29

08/08/ Copy and complete the table for the relative frequency of flipping a coin 50 times Flip Number Head/Tail Relative Frequency 1H0 2T1/2 50

08/08/ GRAPH YOUR RESULTS Compare your results with the first graph you drew. What do you notice?