Produced by MEI on behalf of OCR © OCR 2013 Probability Trees © OCR 2014

Produced by MEI on behalf of OCR © OCR 2013 What do you think the chances of passing both your theory and practical driving tests first time are? © OCR 2014

Produced by MEI on behalf of OCR © OCR 2013 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. © OCR 2014

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. © OCR 2014

Produced by MEI on behalf of OCR © OCR 2013 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? © OCR 2014

Produced by MEI on behalf of OCR © OCR 2013 Number of people848 Number passing318 © OCR 2014 × 6 What do you need to multiply 8 by to get to 48?

Produced by MEI on behalf of OCR © OCR 2013 © OCR 2014 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

Produced by MEI on behalf of OCR © OCR 2013 Tree diagram Pass 48 people Not pass © OCR 2014 Theory first attempt 18 30

Produced by MEI on behalf of OCR © OCR 2013 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. © OCR 2014

Produced by MEI on behalf of OCR © OCR 2013 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? © OCR 2014

Produced by MEI on behalf of OCR © OCR 2013 Number of people318 Number passing16 © OCR 2014 × 6 What do you need to multiply 3 by to get to 18?

Produced by MEI on behalf of OCR © OCR 2013 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 © OCR 2014

Produced by MEI on behalf of OCR © OCR 2013 Tree diagram Pass Not pass 48 people Pass Not pass © OCR 2014 Number passing theory first time Number passing practical first time

Produced by MEI on behalf of OCR © OCR 2013 How many of the 30 people who didn’t pass their theory test first time would you expect to pass the practical first time? © OCR 2014

Produced by MEI on behalf of OCR © OCR 2013 Number of people330 Number passing110 © OCR 2014 × 10 What do you need to multiply 3 by to get to 30?

Produced by MEI on behalf of OCR © OCR 2013 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 © OCR 2014

Produced by MEI on behalf of OCR © OCR 2013 Tree diagram Pass Not pass 48 people Pass Not pass © OCR 2014 Number passing theory first time Number passing practical first time

Produced by MEI on behalf of OCR © OCR 2013 Answering questions You can now use the tree diagram to answer questions on probability. You have all the information you need on it. © OCR 2014

Produced by MEI on behalf of OCR © OCR 2013 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? © OCR 2014

Produced by MEI on behalf of OCR © OCR 2013 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? © OCR 2014