4532.sagews

a=1/4;b=3/4

k1=1/2;k2=1/4;k3=1/4

pC1=a*k1;pC1

1/8

pC2=b*k1+a*k2;pC2

7/16

pC3=b*k2+a*k3;pC3

1/4

pC4=b*k3;pC4

3/16

def bayesFormula(pcm1,pm1,pcm2,pm2):
      # P(M=m|C=c) = P(C=c|M=m)*P(M=m) / ( P(C=c|M=a)*P(M=a) + P(C=c|M=b)*P(M=b) ) 
   return pcm1*pm1/( pcm1*pm1+pcm2*pm2 )

pC1Ma=k1;pC1Mb=0;pC2Ma=k2;pC2Mb=k1;pC3Ma=k3;pC3Mb=k2;pC4Ma=0;pC4Mb=k3

pMaC1=bayesFormula( pC1Ma, a, pC1Mb, b);
pMaC2=bayesFormula( pC2Ma, a, pC2Mb, b);
pMaC3=bayesFormula( pC3Ma, a, pC3Mb, b);
pMaC4=bayesFormula( pC4Ma, a, pC4Mb, b);
[pMaC1,pMaC2,pMaC3,pMaC4]

[1, 1/7, 1/4, 0]

pMbC1=bayesFormula( pC1Mb, b, pC1Ma, a);
pMbC2=bayesFormula( pC2Mb, b, pC2Ma, a);
pMbC3=bayesFormula( pC3Mb, b, pC3Ma, a);
pMbC4=bayesFormula( pC4Mb, b, pC4Ma, a);
[pMbC1,pMbC2,pMbC3,pMbC4]

[0, 6/7, 3/4, 1]