Un point toujours bon à rappeler en calcul de probabilités: les probabilités ne sont pas intuitives. Comme le dit John Cook à propos des experts en probas:

They’ll say things like “I imagine the answer is around this, but I’d have to go through the calculations to be sure.” Probability is not like physics where you can usually get within an order of magnitude of a correct answer without formal calculation. Probabilistic intuition doesn’t take you as far as physical intuition.