1. 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
days
More than
90 days
Under $300,000 39 31 15 85
$300, ,000 35 45 4 84
Over $600,000 8 12 82 80 19
181
Selling price
Total

2. 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
days
More than
90 days
Under $300,000 39 31 15 85
$300, ,000 35 45 4 84
Over $600,000 8 12 82 80 19
181
Selling price
Total

3. 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
days
More than
90 days
Under $300,000 39 31 15 85
$300, ,000 35 45 4 84
Over $600,000 8 12 82 80 19
181
Selling price
Total

4. 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
days
More than
90 days
Under $300,000 39 31 15 85
$300, ,000 35 45 4 84
Over $600,000 8 12 82 80 19
181
Selling price
Total

5. 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
days
More than
90 days
Under $300,000 39 31 15 85
$300, ,000 35 45 4 84
Over $600,000 8 12 82 80 19
181
Selling price
Total

6. 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
days
More than
90 days
Under $300,000 39 31 15 85
$300, ,000 35 45 4 84
Over $600,000 8 12 82 80 19
181
Selling price
Total

7. Blood Group Systems (Rh & K)
Rh system Kell system Outcome Probability
0.81 x 0.08
0.81 x 0.92
0.19 x 0.08
0.19 x 0.92 K+ K–
Rh K+
Rh K–
Rh– K+
Rh– K–
0.08
0.92
Rh+
0.81 K+ K–
0.08
0.92
0.19
Rh–

8. Blood Group Systems (K & Rh)
Kell system Rh system Outcome Probability
0.08 x 0.81
0.08 x 0.19
0.92 x 0.81
0.92 x 0.19
Rh+
Rh–
K Rh+
0. 81
0.19 K+
0.08
K Rh–
Rh+
Rh–
0.81
0.19
K– Rh+
0.92 K–
K– Rh–

9. 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?
98% of 0.01
Test result
7% of 0.99
Disease status
Negative
Positive
Total
Not HIV
HIV
0.0098
0.0002
0.01
0.0693
0.9207
0.99
Total
0.0791
0.9209 1

10. 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?
Test result
Disease status
Negative
Positive
Total
Not HIV
HIV
0.0098
0.0002
0.01
0.0693
0.9207
0.99
Total
0.0791
0.9209 1

11. 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?
/ =
Test result
Disease status
Negative
Positive
Total
Not HIV
HIV
0.0098
0.0002
0.01
0.0693
0.9207
0.99
Total
0.0791
0.9209 1

12. ELISA: HIV Screening Test
Proportion who don’t have HIV (99%)
Proportion who have HIV (1%)
Why is the probability of having HIV given that the test is positive so low?

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

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

15. ELISA: HIV Screening Test
Disease status
Test result
HIV and Pos
HIV and Neg
Not HIV and Pos
Not HIV and Neg
Outcome
Probability
0.98 x 0.01
0.98
0.02
0.07
0.93
Pos | HIV
Neg | HIV
Pos | Not HIV
Neg | Not HIV
HIV
Not HIV
0.01
0.99
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. ELISA: HIV Screening Test
Disease status
Test result
HIV and Pos
HIV and Neg
Not HIV and Pos
Not HIV and Neg
Outcome
Probability
0.98 x 0.01
0.98
0.02
0.07
0.93
Pos | HIV
Neg | HIV
Pos | Not HIV
Neg | Not HIV
HIV
Not HIV
0.01
0.99
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. ELISA: HIV Screening Test
Disease status
Test result
HIV and Pos
HIV and Neg
Not HIV and Pos
Not HIV and Neg
Outcome
Probability
0.98 x 0.01
0.98
0.02
0.07
0.93
Pos | HIV
Neg | HIV
Pos | Not HIV
Neg | Not HIV
HIV
Not HIV
0.01
0.99
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 . 07 01 98 )
Pos |
HIV ( P + =