Let A1 denote asian student, A2 denote american student, A3 denote european student, A4 denote african student, and G denote that a tudent is a girl.
Given
P(A1)=0.3,
P(A2)=0.4,
P(A3)=0.2,
P(A4)=0.1,
P(G∣A1)=0.4,
P(G∣A2)=0.5,
P(G∣A3)=0.6,
P(G∣A4)=0.2
P(G)=P(A1)P(G∣A1)+P(A2)P(G∣A2)+
+P(A3)P(G∣A3)+P(A4)P(G∣A4)=
=0.3(0.4)+0.4(0.5)+0.2(0.6)+0.1(0.2)=0.46
Use the Bayes' Theorem
P(A1∣G)=P(G)P(A1)P(G∣A1)==0.460.3(0.4)=236≈0.260870
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