1. Produced by MEI on behalf of OCR © OCR 2013 Introduction to Quantitative methods Probability and risk © OCR 2014

2. Produced by MEI on behalf of OCR © OCR 2013 In a game show you have just won £5000. You have two options: Roll a dice and if it lands on an even number you win another £5000; if it lands on an odd number you lose your original £5000. or Stick with the £5000. What will you do? © OCR 2014

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

4. Produced by MEI on behalf of OCR © OCR 2013 ©© OOCCRR 20132013 Would you rather have: £1 a week for the next 50 years or A lottery ticket every week for the next 50 years? Produced by MEI on behalf of OCR © OCR 2014

5. Produced by MEI on behalf of OCR © OCR 2013 There is risk involved in the lottery: You might lose your money every week Or You might win millions © OCR 2014

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

7. Produced by MEI on behalf of OCR © OCR 2013 If you bought a lottery ticket every week, on average you would win once every 14 000 000 weeks. This is 269 231 years. © OCR 2014

8. Produced by MEI on behalf of OCR © OCR 2013 Risk is written in terms of probability or in the form 1 in n Risk can also be written in terms of rate….for example death rate. Earthquakes can occur once every n years – that is the risk for earthquakes © OCR 2014

9. Produced by MEI on behalf of OCR © OCR 2013 Death rate is usually expressed as number of deaths per 1000 of the population in a year. (although sometimes as number per 100 000 of population) The death rate in South Africa is 17.49 deaths per 1000 of the population. The death rate in the Philippines is 4.92 deaths per 1000 of the population. Why do you think these are so different? © OCR 2014

10. Produced by MEI on behalf of OCR © OCR 2013 Example In Scotland in 2005, the number of people dying of lung cancer was 4 543. The population of Scotland was 5 094 800. What was the death rate for lung cancer per 100 000 people? This means the number of deaths per 100 000 people. © OCR 2014

11. Produced by MEI on behalf of OCR © OCR 2013 4543 people died out of 5 094 800 The death rate for lung cancer in Scotland is 89 deaths per 100 000 people. © OCR 2014 People5 094 800100100 000 Deaths45430.089289 ÷ 50948 × 1000

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

13. Produced by MEI on behalf of OCR © OCR 2013 © OCR 2014 ÷4543

14. Produced by MEI on behalf of OCR © OCR 2013 Micromorts A micromort is a unit of risk representing a one in a million chance of death. The risk of death from a general anesthetic is estimated to be 1 in 100 000 This would be 10 in 1000 000…..or 10 micromorts. © OCR 2014

15. Produced by MEI on behalf of OCR © OCR 2013 One in a million chance Imagine tossing 20 coins in the air and they all land on heads. Number of outcomes = 2 × 2 × 2 ×……..× 2 = 1 048 576 The chances of all the coins landing on heads is about 1 in a million. © OCR 2014 20 times

16. Produced by MEI on behalf of OCR © OCR 2013 Insurance Insurance is based on risk. Insuring your car means if the car is damaged in an accident you will get some money back to repair it. The more risky something is, the more you would have to pay in insurance. © OCR 2014

17. Produced by MEI on behalf of OCR © OCR 2013 Insurance In 2013, the average price of car insurance for 17- 22 year olds was £1158 per year. Do you think the car insurance for someone aged 47 – 52 is higher or lower than this? Why do you think this is? © OCR 2014