Scores are unnormalized. Dividing by the sum of the shown scores produces exact posteriors that sum to one, then the larger posterior gives the exact argmax.

highlighted = computed this step

Normalize the scores

The denominator is 1/4 + 1/12. Dividing each score by that sum gives posterior A 3/4 and posterior B 1/4.

P(Ax)=3/4,P(Bx)=1/4P(A\mid x)=3/4,\quad P(B\mid x)=1/4
Posteriors and argmaxNormalized posteriors sum to one exactly.Naive Bayes from countstotal=6; counts=A:4, B:2feature counts: F1=1: A=3, B=1; F2=1: A=2, B=1query: F1=1, F2=1; smoothing=noneclassP(c)likelihood count/countscoreposteriorsumargmaxAP(A)=4/6 (=2/3)P(F1=1|A)=3/4P(F2=1|A)=2/4 (=1/2)1/43/41ABP(B)=2/6 (=1/3)P(F1=1|B)=1/2P(F2=1|B)=1/21/121/41posteriors sum = 1argmax=Anaive independence assumed; no smoothing; no logs or decimals

Why the sum check matters

The rendered table shows posteriors sum = 1. This is an exact check that the normalized fractions form one distribution over the shown classes.

P(Ax)+P(Bx)=1P(A\mid x)+P(B\mid x)=1
Posteriors and argmaxNormalized posteriors sum to one exactly.Naive Bayes from countstotal=6; counts=A:4, B:2feature counts: F1=1: A=3, B=1; F2=1: A=2, B=1query: F1=1, F2=1; smoothing=noneclassP(c)likelihood count/countscoreposteriorsumargmaxAP(A)=4/6 (=2/3)P(F1=1|A)=3/4P(F2=1|A)=2/4 (=1/2)1/43/41ABP(B)=2/6 (=1/3)P(F1=1|B)=1/2P(F2=1|B)=1/21/121/41posteriors sum = 1argmax=Anaive independence assumed; no smoothing; no logs or decimals

Summary

The larger posterior is A, so the exact argmax is A. The renderer recomputes that argmax from the displayed count table.

argmaxcP(cx)=A\arg\max_c P(c\mid x)=A
Posteriors and argmaxNormalized posteriors sum to one exactly.Naive Bayes from countstotal=6; counts=A:4, B:2feature counts: F1=1: A=3, B=1; F2=1: A=2, B=1query: F1=1, F2=1; smoothing=noneclassP(c)likelihood count/countscoreposteriorsumargmaxAP(A)=4/6 (=2/3)P(F1=1|A)=3/4P(F2=1|A)=2/4 (=1/2)1/43/41ABP(B)=2/6 (=1/3)P(F1=1|B)=1/2P(F2=1|B)=1/21/121/41posteriors sum = 1argmax=Anaive independence assumed; no smoothing; no logs or decimals