2.13 Review of Level 2 (NZ curriculum) Simulations.

1. SIMULATIONS
2.13 Probability

2. The Idea:
A simulation uses Maths to imitate a real situation
It’s supposed to give similar results
..and so acts as a predictor of what should actually
happen in real life
It is a model in which repeated experiments are
carried out for the purpose of estimating in real life
We use a mathematical tool to generate numbers,
which we map onto real life to estimate results
cheaply and quickly.

3. Simulations…
Are used to solve problems using experiments
when it is difficult to calculate theoretically
Often involve either the calculation of:
• The long-run relative frequency of a
successful event (probability of success)
• The average number of ‘visits’ taken to gain
a ‘full-set’ (I need to make 6 visits)
Sometimes have limits put on them – how many
can I get for $14? How often will I be successful?

4. What are your chances..?
1. If you had a baby, how likely is it
that you would get a girl?
2. If you threw a dice, that you would
get a 6?
3. That I am going to beat up Marcel
before the hour is out?
4. That the next 4 days will be sunny?
What assumptions did you just make?!

5. Things to remember
We are using maths tools to pretend
or “simulate” the real situation.
That way we can predict the
outcome without actually having
to be in the real life situation.

6. Things to remember
1. Tool
2. Trial
3. Assumptions
4. Results
5. Calculations
6. Conclusion

7. TOOL
• This is how we decide what we will simulate the
actual situation with.
• There are many different types of tools available
to us: • Coins
• Dice
• Spinners
• Random number generators
• And many others…
• They all have one thing in common: they are fair.
• When we describe how we use the tool, we must
be specific – write for an idiot!!!!

8. TOOL
1. We are using Ran# on the calc.
2. For 5 items, numbered 10, 11…14 we
would put in
DATA Ran# + STARTER
ie 5 Ran# + 10.
3. Always write ‘ignore decimals’ if
appropriate. We must assume the
person knows nothing
about Mathematics
when we write the
Tool-i.e. be very
specific.

9. TOOL
Which tool would you use to:-
1. Determine the probability of having 3
boys (sex of the child)
2. Find out how many rainy days we should
have had this year? P(rain)=0.2
3. Work out whether an engine on your
plane was going to fail
. 4 engines, P(fail)=40%

10. TRIAL
• Define what ONE trial is.
• Decide how we will stop each trial
•What designates a SUCCESS in the trial.
•We also have to decide HOW MANY
trials are required to be statistically
significant-we usually do between 20
and 30.

11. The Six Dwarfs
Description
A cereal company wants to promote its product.
Inside each box of cereal is one dwarf –
Sneezy, Happy, Grumpy, Bashful, Doc, and Sleepy.
There are equal numbers of each dwarf.
When you have collected all six dwarfs, you can send away
for a life-sized version of the seventh dwarf, Dopey.
Task
Calculate how many boxes of cereal you need to buy on
average to collect all the dwarfs and get Dopey.

12. ASSUMPTIONS
• All events are independent (the outcome
of one event won’t affect the other)
•We have fair tools (ie the coin won’t be
weighted to come up heads)
• If we did the experiment again, we would
probably come up with a slightly different
estimate

13. RESULTS
•We always put our results into a table
as then they are easy to use in the
calculations. (Must show you are organised!)
• Often the table is drawn for you, but
sometimes you will have to draw your own.
• Put in a ‘success’ column if needed.

14. CALCULATION
• Always answer the question!
• This is often an average (mean) or a proportion/probability:
Mean = number of cereal boxes needed
total number of trials
Prob =favourable
total
This will NEVER be bigger
than 1 or 100%!!!
Just sayin’..
• We can also answer expected number (‘how many’)questions
- probability multiplied by number of trials.

15. CONCLUSION
You must state the following at some stage in
your simulation:
My result is only an estimate. If I repeated
this simulation, I would probably get
different results and my estimate would be
different.
ANSWER the question or problem!
Continued …. 

16. CONCLUSION ctd
Give both the maths answer (5.16 – show working!)
and the real life answer (I would need to buy at least 5 boxes
of cereal to get all 4 animals. To be on the safe side, I would advise
someone to buy six boxes, as the mathematical answer is over 5.)
Assumptions – you assume that the tool is FAIR, that
the selection is RANDOM and that each thing has
an equal chance of being chosen.
ELI – effects, limitations, improvements – link to
the real life situation and say how each would
affect your simulation.

17. WHATIFS!!!!
ELI – effects, limitations, improvements – link to
the real life situation and say how each would
affect your simulation.
Whatif…. Come up with a few ideas – use your
imagination! THEN put your Maths Hat on and say
how it would change or affect your simulation or
results or sampling method or… something 
Whatif… someone STOLE all the Goofies?
Whatif .. The machine broke and put in no Spongebobs?
Whatif.. The black dye ran so more Mickeys were discarded?

18. Merit – TTRCA +explain +assumptions
• Tools – link to context and explain why you
allocated certain numbers
• Trial
• Results – explain how you will record results
in the table
• Calculation – use your results to justify your
findings
• Answer – Explain what would happen if you
were to do another simulation
- write about assumptions

19. Excellence – Merit + effects +
improvement
• Tools – link to context and explain why you allocated
certain numbers
• Trial – clearly explain success, linking to context
• Results – explain how you will record results in the
table
• Calculation – use your results to justify your findings
• Answer – Explain what would happen if you were to do
another simulation
- write about assumptions and their effect on the
simulation
- clearly explain how to improve the simulation to
better reflect the context

20. Practice Simulation
• We are in Disneyland and the promoters are
running a Donald Duck promotion.
• Every time you pay for a ride you collect a card
with a picture of one of Donald Duck’s nephews-
Huey, Duey or Louie.
• P(Huey)=0.5, P(Duey)=0.2, P(Louie)=0.3
• When you collect all 3 Ducks, you win a BIG
Donald Duck.

21. Simulate the situation and determine how many rides you
need to go on to collect all 3 ducks and therefore collect your
BIG DUCK prize.
Remember to follow the rules of
1. Tool
2. Trial
3. Assumptions
4. Results
5. Calculation

22. Your second practice
• What is the probability that a 3 child
family will contain exactly 3 boys? You
may assume that a boy or girl is equally
likely to be born.

23. Links and investigations
Tools
• Dice Roller
• Throwing coins
• Drawing playing
cards
• Spinners
• Random number
generator
Sites
• Monty Hall – my favourite!
• Try the cereal box simulation
here
• Birthdays - The answer may
surprise you!

24. Think about this:
Miss Fuller creates the following cards:
H A V E F U N N N N
You choose a card each time you enter a
maths class on time.
When you have collected cards to spell
HAVE FUN you may take the afternoon off.
How many visits, on average, will it take
you?
OOPS – now do it again. BAD Miss Fuller!!