You just returned from a holiday in an exotic country and heard from another traveller about a disease called barking madness which he tells you his brother had some time ago. The risk of infection is apparently low…but better safe than sorry. Let’s get a blood test!

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The result is positive; however you have no symptoms and are feeling well.

Your doctor provides the following additional information:

• About 1 in a 1000 tourists (0.1%), travelling to the country you have just been, get infected by barking madness but initially don’t show any clinical signs.
• Through the test 99 of 100 people that have the disease are detected.
• Of 100 not-infected people 98 are correctly classified as healthy, while two are wrongly diagnosed as being infected.
• Further test to confirm the initial test would a surgical procedure under general anaesthetics including three nights in hospital.
• Mortality of patients infected with the disease is 30%.

What is the probability that based on the blood test and the additional information provided you are indeed infected with barking madness?

ANSWER: We can use two different methods to solve this problem.