Bayes at the Bac’ [and out!]

In the mathematics exam of the baccalauréat my son (and 160,000 other students) took on Tuesday, the probability problem was a straightforward application of Bayes’ theorem. Given a viral test with 99% positives for infected patients and 97% negatives for non-infected patients, in a population with 2% of infected patients, what is the probability that the patient is infected given that the test is positive? (It looks like another avatar of Exercise 1.7  in The Bayesian Choice!) A lucky occurrence, given that I had explained to my son Bayes’ formula earlier this year (neither the math book nor the math teacher mentioned Bayes, incidentally!) and even more given that, in a crash revision Jean-Michel Marin gave him the evening before, they went over it once again! The other problems were a straightforward multiple choice about complex numbers (with one mistake!), some calculus around the functional sequence xⁿe^-x, and some arithmetic questions around Gauss’s and Bezout’s theorems. A few hours after I wrote the above, the (official) news came that this question had been posted on the web prior to the exam by someone and thus that it would be canceled from the exam by the Ministry for Education! The grade will then be computed on the other problems, which is rather unfair for the students. (On the side, the press release from the Ministry contains a highly specious argument that regulation allows for three to five exercises in the exam, hence that there is nothing wrong with reducing the number of exercises to three!) Not so lucky an occurrence, then, and I very deadly hope this will not impact in a drastic manner my son’s result! (Most likely, the grading will be more tolerant and students will not unduly suffer from the action of a very few….)