1. Produced by MEI on behalf of OCR © OCR 2013 Conditional Probability © OCR 2014

2. Produced by MEI on behalf of OCR © OCR 2013 Can you improve your chances of passing your theory test by using an app? © OCR 2014

3. Produced by MEI on behalf of OCR © OCR 2013 A company has produced an app which it thinks will help people pass their driving theory test. Results show that the number of people passing the theory test is higher if they have used the app before sitting the test and that the number of people using the app is roughly equal to those who don’t use it. © OCR 2014

4. Produced by MEI on behalf of OCR © OCR 2013 Will you do some extra work to pass? Toss a coin. If you get a head you will use the app to help. If you get a tail you won’t use the app. © OCR 2014

5. Produced by MEI on behalf of OCR © OCR 2013 Will you pass the theory test first time? This example is different to the last one as this time the second event is dependent on the first one. The probability of passing changes if you use the simulator. This is called conditional probability. © OCR 2014

6. Produced by MEI on behalf of OCR © OCR 2013 If you used the app Throw a dice. If you get 1, 2, 3, 4 or 5 then you pass the test. If you get a 6 then you don’t. © OCR 2014

7. Produced by MEI on behalf of OCR © OCR 2013 If you didn’t use the app Throw 2 dice and add the scores. If you get a total of 2, 3, 4, 5, or 6 then you pass the test. If you get a score of 7, 8, 9, 10, 11 or 12 then you don’t. © OCR 2014

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

9. Produced by MEI on behalf of OCR © OCR 2013 Tree diagram Pass Yes Not pass 72 people Pass No Not pass © OCR 2014 Number using the app Theory test results 36

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

11. Produced by MEI on behalf of OCR © OCR 2013 Tree diagram Pass Not pass 72 people Pass Not pass © OCR 2014 Number passing theory first time Number passing practical first time 36 30 6

12. Produced by MEI on behalf of OCR © OCR 2013 How many of the 36 people who didn’t use the app would you expect to pass the practical first time? © OCR 2014

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

14. Produced by MEI on behalf of OCR © OCR 2013 Answer Answer: 15 to pass and 21 not to pass. © OCR 2014

15. Produced by MEI on behalf of OCR © OCR 2013 Tree diagram Pass Yes Not pass 72 people Pass No Not pass © OCR 2014 Number using the simulator Number passing practical first time 36 30 6 15 21

16. 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

17. Produced by MEI on behalf of OCR © OCR 2013 Why was 72 a good number to start with? When you draw tree diagrams you may have to decide a number of people to start with. The first probability was out of 2 (halves) and 72 divides by 2 to give 36. The second probabilities were out of 36 and 6 and 36 divides by 36 and 6. 72 was a good number of students to choose as it divides by 2 and the result divides by 6 and 36 © OCR 2014