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résultats d'un test} -\date{Avril 2022} +\date{mai 2023} \pagestyle{empty} @@ -32,7 +32,7 @@ Ce tableau est appelé \textbf{tableau de contingence.} \end{minipage} \begin{minipage}{0.5\linewidth} - \textbf{Critères de fiabilités} + \textbf{Critères de fiabilités} \begin{itemize} \item Sensibilité: probabilité qu'une personne infectée soit testée positive \[ @@ -48,7 +48,7 @@ \end{definition} \begin{doc}{Test médical} - Un médecin cherche à déterminer si une IA est fiable. Pour cela, il a choisi 1000 dossiers de patients dont il sait que 92 d'entres eux souffrent d'un cancer. L'IA quand à elle détecte 862 cas négatif. Parmi ces cas négatifs détectés, le médecin sait que 7 d'entre eux sont malade. + Un médecin cherche à déterminer si une IA est fiable. Pour cela, il a choisi 1000 dossiers de patients dont il sait que 92 d'entres eux souffrent d'un cancer. L'IA quand à elle détecte 862 cas négatif. Parmi ces cas négatifs détectés, le médecin sait que 7 d'entre eux sont malades. Pour déterminer si une assistance est fiable, il faut que la sensibilité soit supérieur à 90\%. \end{doc} @@ -94,4 +94,43 @@ \end{enumerate} \end{multicols} +\pagebreak + +\textbf{Tests Covid} + +En 2020, on pouvait lire l'article suivant dans le monde. + +Dans la suite on note $P=$"test positif" et $I=$"patient infecté". +\begin{enumerate} + \item Chercher dans l'article les valeurs de la sensibilité et de la spécificité du test Covid. Puis traduire ces valeurs en terme de probabilités. + \item On se place dans le premier cas où 1\% de la population est infecté. + + \begin{minipage}{0.5\linewidth} + \begin{enumerate} + \item On étudie une population de 1000 individus. Compléter le tableau suivant + + \item Calculer la probabilité que parmi les testés positifs, le patient ne soit pas infecté. + \item Calculer la probabilité que parmi les testés négatif, le patient ne soit pas infecté. + \end{enumerate} + \end{minipage} + \hfill + \begin{minipage}{0.4\linewidth} + \begin{tabular}{|*{3}{c|}c|} + \hline + & infecté & non infecté & total \\ + \hline + Test positif & & & \\ + \hline + Test négatif & & & \\ + \hline + total & & & 1000 \\ + \hline + \end{tabular} + \end{minipage} + \item Mêmes questions pour le cas où 10\% de la population est infectée. + \item Mêmes questions pour le cas où 30\% de la population est infectée. + \item Que pensez-vous de ces tests? +\end{enumerate} + +\includegraphics[scale=0.5, angle=90]{./fig/resultat_test} \end{document} diff --git a/Enseignement_Scientifique/03_Informatique_et_IA/fig/resultat_test.jpg b/Enseignement_Scientifique/03_Informatique_et_IA/fig/resultat_test.jpg new file mode 100644 index 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