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Simple Simulations
Discuss with your teacher how you can toss coins to make up
families of boys and girls, and how you can play book cricket.
These are simulations where you don't look at real families or
play real cricket. You set up a system which copies the main
features of the real thing.
Collecting Cards
You will need a pack of cards and page R1.
Have you ever collected a set of cards or medals? They can be
given with packets of tea or cornflakes, or with a gallon of
petrol. You often get the same card more than once.
There is one card in each packet of tea.
About how many packets of tea would you need for a set with:
| a |
One card |
| b |
Two cards |
| c |
Four cards |
Instead of actually buying packets of tea you can try this
experiment, called a SIMULATION.
Imagine that you are collecting a set of four playing cards,
one of each suit.
Follow the instructions below carefully. Use Table 2 on page R1
to record your results.
| d |
Turn out your pack of cards.
Guess the number of cards you think you will need to make
a complete set.
Write down your guess on the second column of Table 2.
Shuffle the pack.
Turn over the cards one at a time. Place them in piles
according to suit.
STOP as soon as you have at least one card of each suit.Count
the total number of cards you have put down.
Write down that number in the last column.
Replace the cards in the pack.
Repeat the experiment until you have 10
results.
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Your teacher will collect your results.
Describing the Results
| a |
Find the MEAN of the 10 results.
(To do this add up the numbers in the last
column and divide by 10.) |
| b |
Write down the smallest number of cards you
needed.
Write down the largest number of cards you needed.
Find the RANGE for your 10 results.
(To do this take the smaller number away from the larger
one.) |
| c |
What fraction of your 10 results needed fewer
than
six cards? |
| d |
What fraction needed more than 10 cards? |
| e |
What fraction needed exactly seven cards? |
| f |
Find the mean and range of the class results. |
| g |
How has this experiment helped you to decide how
many packets you need buy to get a complete set? |
Is there Room on the Bus?
You will need a six-sided die, and page R1.
Albert Ward runs a minibus from his village to a local town.
The bus has 10 seats. On market days it is very popular and more
than 10 people want to book seats.
However, some of the people who book do not come. Empty seats
mean less profit. Albert has found that about one person in six
does not come. So he decides to take more than 10 bookings. He
expects some people not to come.
How many bookings do you think he should take?
What problems could this number of bookings cause?
Before overbooking, he tries a simulation with 12 bookings for
each trip. He knows that:
the minibus has 10 seats,
12 people have booked a seat,
in the past about one person in six has not come.
It is not possible to say which person will not come. We say
there is one chance in six that a particular person will not
come. We can simulate this by throwing a die:
The person comes if you get 2,3,4,5,6.
The person does not come if you get 1.
Simulate five trips with 12 seats booked. Record your results
in Table 3 on page R1.
| a |
For each trip throw a die 12
times to see which of the 12 people come. Put a tick if
the person comes and a cross if not. Add up the number of
ticks for each trip and write this number in the next
column. If more than 10 people come, put a tick in the
last column. |
Your teacher will collect your results.
| b |
How many of your five trips are overbooked by
one seat?
How many by two seats?
How many are just right?
How many have one or more spare seats? |
| c |
Do you think the minibus owner would be happy
with this result?
Why? |
| d |
Using the class results, find the fraction of
trips overbooked.
What do you think Albert should do? |
| e |
Do you think this simulation is like Albert's
problem?
How does it differ?
How could we improve the simulation? |
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