produced by mei on behalf of ocr © ocr 2013 probability trees © ocr 2014

Produced by MEI on behalf of OCR © OCR 2013 Produced by MEI on behalf of OCR © OCR 2013

Probability Trees

© OCR 2014


What do you think the chances of passing both your theory and practical driving tests first time are?

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To pass your driving test you must pass two parts – the theory test and the practical test. You can’t sit your practical test until you have passed your theory test.

You are going to simulate this.

The simulation is based on realistic probabilities and it assumes passing the theory test and practical test are independent.

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Produced by MEI on behalf of OCR © OCR 2013

Simulating whether you will pass the theory test first time

Toss three coins.

If you get 2 heads and a tail you pass your theory first time.

If you get anything else you need more than 1 attempt to pass.

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Theory test

What is the probability of getting 2 heads and 1 tail?

If you had 48 people how many would you expect to pass first time?

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Number of people 8 48

Number passing 3 18

The probability of passing the theory first time is

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× 6

× 6

What do you need to multiply 8 by to get

to 48?

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We expect 18 people to pass their theory test first time.

How many people would you expect not to pass?

Fill these in the probability tree


Tree diagram

Pass

48 people

Not pass

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Theory first attempt

18

30


Simulating whether you pass the practical first time

Roll a dice.

If you get a 1 or a 2 you pass your practical test first time.

If you get a 3, 4, 5 or 6 you need more than 1 attempt to pass your practical test.

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Practical test

What is the probability of getting a 1 or 2?

Out of the 18 who passed the theory first time how many would you expect to pass the practical first time?

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The probability of passing the practical first time is


Number passing 1 6

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× 6

× 6

What do you need to multiply 3 by to

get to 18?


Out of the 18 people who passed the theory first time how many people do you expect not to pass the practical first time?

Put these 2 pieces of information in the tree diagram

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Tree diagram

Pass

Pass

Not pass

48 people

Pass

Not pass

Not pass

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Number passing theory first time

Number passing practical first time

18

30

6

12


How many of the 30 people who didn’t pass their theory test first time would you expect to pass the practical first time?

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How many of the 30 people who didn’t pass their theory test first time would you expect not to pass the practical first time?

Put these 2 pieces of information on the tree diagram

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Tree diagram

Pass

Pass

Not pass

48 people

Pass

Not pass

Not pass

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Number passing theory first time

Number passing practical first time

18

30

6

12

10

20


Answering questionsYou can now use the tree diagram to answer questions on probability.

You have all the information you need on it.

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Why was 48 a good number to start with ?

Are there any other numbers that would have been good to start with?

If your probability was in percentages, what number would you start with?

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Government statistics show that in 2011 the proportion of people who passed their theory test at the first attempt was 41%

The proportion of people who passed their practical test first time was 34%

Was this a good simulation? Can you think of any changes to make it more accurate?

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produced by mei on behalf of ocr © ocr 2013 probability trees © ocr 2014

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