Finally, here is the solution to this enigma... I hope you enjoyed it, and that you'll enjoy the one of this week...
It is natural to think that M. Doisy is wrong since there are only 50 persons in the classroom, and there are 365 day per year. But if we consider the complementary event, which means the probability that nobody from these 50 pupils was born the same day. It means that the first one could be born on one of the 365 days, the second one on one of the 364 remaining days, the third one has only 363 possibilities and so on. Until we reach the 50th student who has only 365 - 49 = 316 possibilities left. Then, the favourable case number is 365x364x363x...x317x316. And the number of total cases of birth possible is 365x365...x365 (Everyone was born on one day of the year). Eventually, the probability of nobody to be born the same day would be the ration between this two numbers which is near to
0.0296. So the probability of two pupils to be born on the same day is 1 - 0.0296 = 0.97 which means 97 % !!
M. Doisy has 97% of chance to tell the truth. If we thought he was wrong, it's because we confused his affirmation with the one that pretends that a pupil was born on the same day as him. In this case, the date is fixed, and the probability is really inferior to his one.
Congratulations to Thibault, Charlotte and Florian who managed to find the solution.
