19/04/23 1S. Berg

DESCRIBING SIMULATIONS

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T T R CTool: - 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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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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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:

- Repeat for 30 trials

Calculation: PROB OF PASS= Nos successful trials 30

Trial Outcome Result

1 1,5,8,7,9,6,2,7 X

2 7,4,9,2,3,1,6,5 √

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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:

- Repeat for 30 trials

Calculation: PROB OF EMBARRASSEMNENT = Nos successful trials 30

Trial Outcome Result

1 4,5,8,7,9,6,2,7,10,9 Embarrassed

2 7,4,9,2,3,2,6,5,8,7Not

Embarrassed

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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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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

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Results:

- Repeat for 30 trials

Calculation: E(Boxes of Cereal)= Sum of Results Column 30

Trial Outcome Result

1 1,5,3,6,4,5,4,2 8

2 6,5,3,5,4,6,1,3,2 9

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Copy and complete the table for the relative frequency of flipping

a coin 50 times

Flip NumberHead/Tail

Relative Frequency

1 H 0

2 T 1/2

50

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GRAPH YOUR RESULTS

Compare your results with the first graph you drew.

What do you notice?