### This question achieved fame because a study in 1982 asked doctors a similar question, and 95% of those surveyed answered wrongly - and not just slightly wrongly, but off by ten times. We could find the answer to the above question using Bayes' rule, but here, we'll tackle it using Invrea Scenarios. Consider the following spreadsheet: ### In this model, cell F4 is 1 if the patient in question has cancer, and cell G4 is 1 if the detector gives a positive result. By right-clicking cell G4 and recording an actual value of 1, as we explained in our previous blog posts, we focus our attention on only cases where the detector gives a positive result (Note that this has already been done in the demonstration spreadsheet). Given that, to find the probability that the patient has cancer, we can simply run 50,000 simulations and plot the result of cell F4: ### Spreadsheet model for the impact of passing in football ### By using Invrea Scenarios, we can easily validate Reep's observation that the majority of goals occur after a small number of passes. The following is a plot of the average number of passes before a goal, over 15,000 simulations: ### However, if we plot the average number of passes overall against the goals scored over the whole game, we see a very different story: ### This heatmap shows us that as the number of goals scored goes up, the average pass length is likely to as well. This effect can be seen more plainly using the techniques explained in our previous blog posts, if we condition on at least five goals being scored, and then plot the posterior distribution over the average number of successful subsequent passes of teams that manage to score at least five goals. The distribution over pass lengths leans to the right, indicating that longer average pass lengths correlate with more goals scored: 