Usuario:Stoni/Superprogesteron

1.

$P(B|A)=P(P_{+}|E_{+})={\frac {P(E_{+}|P_{+})P(P_{+})}{P(E_{+}|P_{+})P(P_{+})+P(E_{+}|P_{-})P(P_{-})}}={\frac {{\frac {8}{9}}{\frac {9}{20}}}{{\frac {8}{9}}{\frac {9}{20}}+{\frac {4}{11}}{\frac {11}{20}}}}={\frac {2}{3}}$

2.

$P(B)=P(P_{+})=P(P_{+}|E_{+})P(E_{+})+P(P_{+}|E_{-})P(E_{-})={\frac {8}{12}}{\frac {12}{20}}+{\frac {1}{8}}{\frac {8}{20}}={\frac {9}{20}}$

3.

$P(A|B)=P(E_{+}|P_{+})={\frac {P(P_{+}|E_{+})P(E_{+})}{P(P_{+}|E_{+})P(E_{+})+P(P_{+}|E_{-})P(E_{-})}}={\frac {{\frac {8}{12}}{\frac {12}{20}}}{{\frac {8}{12}}{\frac {12}{20}}+{\frac {1}{8}}{\frac {8}{20}}}}={\frac {8}{9}}$

Si vemos en la tabla hay 9 enfermos de P+ de los cuales 8 tienen tambien E+. Osea que los claculos son correctos.