Lösungen/Solutions/F2S1Ue/Ex13

L = Lektion/ Leçon   -- Sprechstunde / heures de consultation
W = Work / Arbeit / Travail
A=Anhang/Annexe/Appendice

Ueb/Ex 1      W

A ⋂ B = {},   A ⋃ B = Ω
X= Ereignis Schwarzfahrer zu ergreifen = événement de trouver un sans billet
a = P(X|A),  b = P(X|B)
aA=P(A);    bB=P(B);    xX=P(X)
X=(A⋂X)⋃(B⋂X);   (A⋂X)⋂(B⋂X)={};
P(X)=P(A⋂X)+P(B⋂X);
P(A⋂X) = P(A) P(X|A);
P(B⋂X) = P(B) P(X|B);

a = 0.1;  b = 0.02;
aA = 4000/(4000 + 2000);  
    bB = 2000/(4000 + 2000);
xX = aA * a  +  bB * b

Ueb/Ex 2      W

c=P(X|C);  cC=P(C);
P(C⋂X)=P(X)*P(C|X)=P(C)*P(X|C)
d=P(C|X)= P(C)*P(X|C)/P(X)= P(C)*P(X|C)/(P(A⋂X)+P(B⋂X)+P(C⋂X))
= P(C)*P(X|C)/( P(A) P(X|A)+ P(B) P(X|B)+ P(C) P(X|C))
=cC * c /(aA * a + bB * b + cC * c)

aA = 4000/(1000 + 4000 + 2000);
bB = 2000/(1000 + 4000 + 2000);
cC = 1000/(1000 + 4000 + 2000);
a = 0.1;  b = 0.02;
c = 0.015;

d = cC*c/(aA*a + bB*b + cC*c)