DESCRIBING SIMULATIONS 1212020 S Berg 1 TTRC Tool

DESCRIBING SIMULATIONS 12/1/2020 S. Berg 1

TTRC 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 12/1/2020 Number of trials 2

TRUE - FALSE TEST PROBLEM n n Paul has not studied for 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. n 12/1/2020 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) 3

Soln - True - False test problem Tool: -CALCULATOR (10 Ran# +1) -(RAN# =OPTN / F 6 / F 3 / F 4 / F 1) 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 12/1/2020 4

Results: Trial 1 2 Outcome 1, 5, 8, 7, 9, 6, 2, 7 7, 4, 9, 2, 3, 1, 6, 5 Result X √ - Repeat for 30 trials Calculation: 12/1/2020 PROB OF PASS= Nos successful trials 30 5

MINIBUS PROBLEM n n n 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. 12/1/2020 6

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 12/1/2020 7

Results: Trial Outcome Result 1 4, 5, 8, 7, 9, 6, 2, 7, 10, 9 Embarrassed 2 Not Embarrassed 7, 4, 9, 2, 3, 2, 6, 5, 8, 7 - Repeat for 30 trials Calculation: 12/1/2020 PROB OF EMBARRASSEMNENT = Nos successful trials 30 8

CEREAL CARDS n n 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. n 12/1/2020 Design a simulation to calculate the EXPECTED NUMBER of cereal boxes you would have to buy to obtain a complete set of six coupons. 9

Soln - CEREAL CARDS Tool: -CALCULATOR (6 Ran# +1) 1 to 6 = Each of the 6 different cards Trial: 12/1/2020 - One trial = generating random numbers until you have at least one of each number 10

Results: Trial Outcome Result 1 2 1, 5, 3, 6, 4, 5, 4, 2 6, 5, 3, 5, 4, 6, 1, 3, 2 8 9 - Repeat for 30 trials Calculation: 12/1/2020 E(Boxes of Cereal)= Sum of Results Column 30 11

Copy and complete the table for the relative frequency of flipping a coin 50 times Head/Tail Relative Frequency 1 H 0 2 T 1/2 Flip Number 12/1/2020 50 12

GRAPH YOUR RESULTS n n 12/1/2020 Compare your results with the first graph you drew. What do you notice? 13