Transcript Describing a simulations

DESCRIBING
SIMULATIONS
10/04/2015
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
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Number of trials
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TRUE - FALSE TEST PROBLEM


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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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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
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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:
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PROB OF PASS= Nos successful trials
30
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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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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
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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:
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PROB OF EMBARRASSEMNENT = Nos successful trials
30
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CEREAL CARDS
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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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Soln - CEREAL CARDS
Tool:
-CALCULATOR (6 Ran# +1)
1 to 6 = Each of the 6 different cards
Trial:
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- One trial = generating random numbers until you
have at least one of each number
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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:
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E(Boxes of Cereal)= Sum of Results Column
30
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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
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50
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GRAPH YOUR RESULTS
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
Compare your results with
the first graph you drew.

What do you notice?
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