Mathematics · University
Bayes rule for an abstract classifier
Use the base rate and both conditional likelihoods. This is an abstract classification model, not a medical test.
Method and conditions
Use the base rate and both conditional likelihoods. This is an abstract classification model, not a medical test.
P(A|B) = P(B|A)P(A)/P(B)
Worked examples
In an abstract classifier, P(A)=0.6, P(B|A)=0.8, and P(B|not A)=0.2. Calculate P(A|B). Round the final result to 4 decimal places if needed.
Total probability gives P(B) = 0.6(0.8) + (1 − 0.6)(0.2). Divide P(A and B) = 0.48 by this total.
0.8571
In an abstract classifier, P(A)=0.5, P(B|A)=0.7, and P(B|not A)=0.3. Calculate P(A|B). Round the final result to 4 decimal places if needed.
Total probability gives P(B) = 0.5(0.7) + (1 − 0.5)(0.3). Divide P(A and B) = 0.35 by this total.
0.7
Try it
In an abstract classifier, P(A)=0.4, P(B|A)=0.5, and P(B|not A)=0.4. Calculate P(A|B). Round the final result to 4 decimal places if needed.
In an abstract classifier, P(A)=0.6, P(B|A)=0.5, and P(B|not A)=0.2. Calculate P(A|B). Round the final result to 4 decimal places if needed.
Check your work
Answers and marking notes
- 0.4545
Total probability gives P(B) = 0.4(0.5) + (1 − 0.4)(0.4). Divide P(A and B) = 0.2 by this total.
- 0.7895
Total probability gives P(B) = 0.6(0.5) + (1 − 0.6)(0.2). Divide P(A and B) = 0.3 by this total.
Further reading and review references
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