1. DESCRIBING SIMULATIONS
20/11/2018
S. Berg

2. 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
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3. 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)
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4. 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
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MEAN = Sum of trial results
Number of trials

5. 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
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6. 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.
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7. 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 numbers from 4 to 10 inclusive
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MEAN = Sum of trial results
Number of trials

8. 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
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9. 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.
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10. 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
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MEAN = Sum of trial results
Number of trials

11. 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
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12. 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
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13. GRAPH YOUR RESULTS Compare your results with the first graph you drew.
What do you notice?
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