# probabilities

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```					                                            Pandemic or Panic?
Probability of infection "1 in 4 million"
Test accuracy 90%

Let I be being infected and I/ be not infected
Let T be "testing positive" and T / be "testing negative"

Click on the following buttons to identify the probabilities you can find from the information

Type in the probabilities and check them

Don't reset this sheet before you have completed the calculations
d from the information

ed the calculations
Working with numbers (you need to complete the probabilities sheet first)
Since the probability of infection is "1 in 4 million" it might be worth imagining that you have some mu
4 million people to test. Type in a possible number to see if it is suitable.

Suggested number of test subjects:

Calculate the number of infected and non-infected people

Infected                                       Not infected

Now find out how many of each of the infected and non-infected people tested positive

Use these results to find the probabilities you need (these can be entered as a fraction by typing = first)

P(I/T) =                                         P(I//T) =
robabilities sheet first)
gining that you have some multiple of

sted positive

Total

as a fraction by typing = first)
Tree diagram

You know P(T/I) and P(T/I/) from the information so the first decision when drawing the tree diagram is "w
goes at the end of the first branches - Infected & Not Infected OR Test Positive & Test Negative?"

Choose which one you think is correct

Fill in the probabilities on the tree diagram

Infected?                         Test
T (+ve)
I
T/ (-ve)

T (+ve)
/
I
T/ (-ve)
sion when drawing the tree diagram is "what
Test Positive & Test Negative?"

Use the tree diagram to find

P(I) =
P(T/I) =
P(T) =

Now use the formula
P( I )  P(T / I )
P( I / T ) 
P(T )
to find
P(I/T) =

now find
P(I//T) =
Two way table
You need to fill in the table carefully. Look at the model carefully before entering the probabilities.

infection state
Infected (I)               Not Infected (I/)
t      Positive (T)         P(I∩T) = P(I) x P(T/I)       P(I/∩T) = P(I/) x P(T/I/)
tes       Negative (T/)       P(I∩T/) = P(I) x P(T//I)     P(I/∩T/) = P(I/) x P(T//I/)
Total              P(I)                         P(I/)

You can fill in the table using the values P(I), P(I/), P(T/I) and P(T/I/) that you know already
Put them in and then press check 1
infection state
Infected (I)               Not Infected (I/)
Positive (T)
t
tes       Negative (T/)
Total
try again
Once you have entered all of the values you know, you can calculate the others
Find the missing values in each column by using the total at the bottom of the column
Find P(S) and P(F) by adding up along the rows.
Complete the table and press check 2
Click the appropriate buttons to highlight the calculations you need.
y before entering the probabilities.

P(T)
P(T/)

try again
try again

ttom of the column
Extension
1       80
In this extension activity, you will find out how worried we should be for different infection rates and t
reliabilities. The minimum P(infected) = 0.000001 which is 1 in 1 million the maximum P(I) = 0.01

Probability of being infected           0.0000010000

Reliability of test                           80         % accurate

After testing
For those with positive results                     For those with negative results

P(infected) =       0.0000040000                 P(infected) =      0.0000000025
P(not infected) =     0.9999960000               P(not infected) =    0.9999999975
Start by keeping the test 80% accurate.
Adjust the probability of being infected - use the max/min/mid buttons to jump quickly.
When do you start to worry?
Now change the reliability of the test and start again with the probability set to it's maximum value.
When is there cause for concern now?
What advice would you give to a government think tank looking into screening for bird flu?
different infection rates and test
the maximum P(I) = 0.01

negative results

0.0000000025
0.9999999975

to jump quickly.

y set to it's maximum value.

ening for bird flu?

```
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 views: 3 posted: 4/24/2010 language: English pages: 14