1. YEAR 13 STATISTICS & MODELLING WORKSHOP DEPARTMENT OF STATISTICS House Sales What proportion of the houses that sold for over $600,000 were on the market for less than 30 days? Days on the market Less than 30 days 30 - 90 daysMore than 90 days Under $300,000 39311585 $300,000 - 600,000 3545484 Over $600,000 84012 828019181 Selling priceTotal

2. YEAR 13 STATISTICS & MODELLING WORKSHOP DEPARTMENT OF STATISTICS Days on the market Less than 30 days 30 - 90 daysMore than 90 days Under $300,000 39311585 $300,000 - 600,000 3545484 Over $600,000 84012 828019181 Selling priceTotal House Sales What proportion of the houses that sold for over $600,000 were on the market for less than 30 days?

3. YEAR 13 STATISTICS & MODELLING WORKSHOP DEPARTMENT OF STATISTICS Days on the market Less than 30 days 30 - 90 daysMore than 90 days Under $300,000 39311585 $300,000 - 600,000 3545484 Over $600,000 84012 828019181 Selling priceTotal House Sales What proportion of the houses that sold for over $600,000 were on the market for less than 30 days?

4. YEAR 13 STATISTICS & MODELLING WORKSHOP DEPARTMENT OF STATISTICS House Sales What is the probability a house sold for under $300,000 given that it sold in less than 30 days? Days on the market Less than 30 days 30 - 90 daysMore than 90 days Under $300,000 39311585 $300,000 - 600,000 3545484 Over $600,000 84012 828019181 Selling priceTotal

5. YEAR 13 STATISTICS & MODELLING WORKSHOP DEPARTMENT OF STATISTICS Days on the market Less than 30 days 30 - 90 daysMore than 90 days Under $300,000 39311585 $300,000 - 600,000 3545484 Over $600,000 84012 828019181 Selling priceTotal House Sales What is the probability a house sold for under $300,000 given that it sold in less than 30 days?

6. YEAR 13 STATISTICS & MODELLING WORKSHOP DEPARTMENT OF STATISTICS House Sales What is the probability a house sold for under $300,000 given that it sold in less than 30 days? Days on the market Less than 30 days 30 - 90 daysMore than 90 days Under $300,000 39311585 $300,000 - 600,000 3545484 Over $600,000 84012 828019181 Selling priceTotal

7. YEAR 13 STATISTICS & MODELLING WORKSHOP DEPARTMENT OF STATISTICS Blood Group Systems (Rh & K) Rh system Kell system Outcome Probability Rh+ Rh – 0.81 0.19 K+ K–K– K–K– 0.08 0.92 0.08 0.92 Rh+ K+ Rh+ K – Rh– K+ Rh– K – 0.81 x 0.08 0.81 x 0.92 0.19 x 0.08 0.19 x 0.92

8. YEAR 13 STATISTICS & MODELLING WORKSHOP DEPARTMENT OF STATISTICS Blood Group Systems (K & Rh) Kell system Rh system Outcome Probability K+ K–K– 0.08 0.92 Rh+ Rh – Rh+ Rh – 0. 81 0.19 0.81 0.19 K+ Rh+ K+ Rh – K– Rh+ K– Rh – 0.08 x 0.81 0.08 x 0.19 0.92 x 0.81 0.92 x 0.19

9. YEAR 13 STATISTICS & MODELLING WORKSHOP DEPARTMENT OF STATISTICS ELISA: HIV Screening Test  98% true positive and 7% false positive  Suppose 1% of the population have HIV  Of those that test positive for HIV, what proportion have HIV? 1 0.99 0.01 Total Not HIV HIV TotalNegativePositive Test result Disease status 98% of 0.01 0.0098 0.0002 7% of 0.99 0.0693 0.9207 0.0791 0.9209

10. YEAR 13 STATISTICS & MODELLING WORKSHOP DEPARTMENT OF STATISTICS ELISA: HIV Screening Test  98% true positive and 7% false positive  Suppose 1% of the population have HIV.  Of those that test positive for HIV, what proportion have HIV? 1 0.99 0.01 Total Not HIV HIV TotalNegativePositive Test result Disease status 0.0098 0.0002 0.0693 0.9207 0.0791 0.9209

11. YEAR 13 STATISTICS & MODELLING WORKSHOP DEPARTMENT OF STATISTICS ELISA: HIV Screening Test  98% true positive and 7% false positive  Suppose 1% of the population have HIV.  Of those that test positive for HIV, what proportion have HIV? 1 0.99 0.01 Total Not HIV HIV TotalNegativePositive Test result Disease status 0.0098 0.0002 0.0693 0.9207 0.0791 0.9209 0.0098 / 0.0791 = 0.1239

12. YEAR 13 STATISTICS & MODELLING WORKSHOP DEPARTMENT OF STATISTICS ELISA: HIV Screening Test Why is the probability of having HIV given that the test is positive so low? Proportion who don’t have HIV (99%) Proportion who have HIV (1%)

13. YEAR 13 STATISTICS & MODELLING WORKSHOP DEPARTMENT OF STATISTICS ELISA: HIV Screening Test Why is the probability of having HIV given that the test is positive so low? Proportion who have HIV (1%) Positive tests Proportion who don’t have HIV (99%) 98% of 1%

14. YEAR 13 STATISTICS & MODELLING WORKSHOP DEPARTMENT OF STATISTICS ELISA: HIV Screening Test Why is the probability of having HIV given that the test is positive so low? Proportion who have HIV (1%) Proportion who don’t have HIV (99%) Positive tests 98% of 1% 7% of 99% True False Many more false positives than true positives

15. YEAR 13 STATISTICS & MODELLING WORKSHOP DEPARTMENT OF STATISTICS ELISA: HIV Screening Test HIV Not HIV 0.01 0.99 Disease status Test result 0.98 0.02 0.07 0.93 Pos | HIV Neg | HIV Pos | Not HIV Neg | Not HIV HIV and Pos HIV and Neg Not HIV and Pos Not HIV and Neg Outcome Probability 0.98 x 0.01 0.02 x 0.01 0.07 x 0.99 0.93 x 0.99 Of those that test positive for HIV, what proportion have HIV? P(HIV Pos) = P(Pos | HIV) x P(HIV)

16. YEAR 13 STATISTICS & MODELLING WORKSHOP DEPARTMENT OF STATISTICS ELISA: HIV Screening Test HIV Not HIV 0.01 0.99 Disease status Test result 0.98 0.02 0.07 0.93 Pos | HIV Neg | HIV Pos | Not HIV Neg | Not HIV HIV and Pos HIV and Neg Not HIV and Pos Not HIV and Neg Outcome Probability 0.98 x 0.01 0.02 x 0.01 0.07 x 0.99 0.93 x 0.99 Of those that test positive for HIV, what proportion have HIV?

17. YEAR 13 STATISTICS & MODELLING WORKSHOP DEPARTMENT OF STATISTICS ELISA: HIV Screening Test HIV Not HIV 0.01 0.99 Disease status Test result 0.98 0.02 0.07 0.93 Pos | HIV Neg | HIV Pos | Not HIV Neg | Not HIV HIV and Pos HIV and Neg Not HIV and Pos Not HIV and Neg Outcome Probability 0.98 x 0.01 0.02 x 0.01 0.07 x 0.99 0.93 x 0.99 Of those that test positive for HIV, what proportion have HIV? 99.007.001.098.0 01.098.0 )Pos|HIV(P    