cjauvin/probs.org

Last active August 30, 2018 16:38

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Concepts de base en prob

Soleil/Pluie	non	oui	total
oui	75	2	77
non	10	13	23
total	85	15	100

Il fait soleil 77% du temps, et il pleut 15% du temps (les deux ne sont pas mutuellement exclusifs).

Joint:

P(Soleil + !Pluie) = 75/100

Marginal:

P(Soleil) = P(Soleil, !Pluie) + P(Soleil, Pluie) = 75/100 + 2/100 = 77/100
P(!Pluie) = P(Soleil, !Pluie) + P(!Soleil, !Pluie) = 75/100 + 10/100 = 85/100

Conditional:

P(Soleil | !Pluie) = P(Soleil, !Pluie) / P(!Pluie) = 75/100 / 85/100 = 0.882
P(!Pluie | Soleil) = P(Soleil, !Pluie) / P(Soleil) = 75/100 / 77/100 = 0.974

Bayes:

P(Soleil | !Pluie) = P(!Pluie | Soleil) * P(Soleil) / P(!Pluie) = 0.974 * 0.77 / 0.85 = 0.882
P(!Pluie | Soleil) = P(Soleil | !Pluie) * P(!Pluie) / P(Soleil) = 0.882 * 0.85 / 0.77 = 0.974

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