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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 So you start with the following probabilities 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/) ) that you know already 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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possible outcomes, probability theory, probability distributions, the experiment, conditional probabilities, imprecise probabilities, random variable, Binomial Probabilities, sample space, the normal

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views: | 3 |

posted: | 4/24/2010 |

language: | English |

pages: | 14 |

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