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 daysMore than 90 days Under $300, $300, , Over $600, Selling priceTotal

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

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

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 daysMore than 90 days Under $300, $300, , Over $600, Selling priceTotal

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

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 daysMore than 90 days Under $300, $300, , Over $600, Selling priceTotal

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

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

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? Total Not HIV HIV TotalNegativePositive Test result Disease status 98% of % of

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? Total Not HIV HIV TotalNegativePositive Test result Disease status

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? Total Not HIV HIV TotalNegativePositive Test result Disease status / =

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%)

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%

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

YEAR 13 STATISTICS & MODELLING WORKSHOP DEPARTMENT OF STATISTICS ELISA: HIV Screening Test HIV Not HIV Disease status Test result 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 x x x 0.99 Of those that test positive for HIV, what proportion have HIV? P(HIV Pos) = P(Pos | HIV) x P(HIV)

YEAR 13 STATISTICS & MODELLING WORKSHOP DEPARTMENT OF STATISTICS ELISA: HIV Screening Test HIV Not HIV Disease status Test result 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 x x x 0.99 Of those that test positive for HIV, what proportion have HIV?

YEAR 13 STATISTICS & MODELLING WORKSHOP DEPARTMENT OF STATISTICS ELISA: HIV Screening Test HIV Not HIV Disease status Test result 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 x x x 0.99 Of those that test positive for HIV, what proportion have HIV? )Pos|HIV(P    