BitWithBite
Mathematics Worksheet
🔁 Bayes' Theorem
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Apply Bayes' theorem.Use the law of total probability.Compute a posterior probability.Understand false positives with rare conditions.📚 Quick Recap
Bayes' Theorem lets us reverse a conditional probability — using what we know about P(B|A) to figure out P(A|B), which is invaluable when direct evidence is hard to obtain.
🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1If P(A)=0.05, P(B|A)=0.7, P(B)=0.15, then P(A|B) =:
2Disease 3%, true-positive 85%, false-positive 10%. P(positive test) =:
3Using that, P(has disease | tests positive) =:
4Bayes shows accurate tests can produce many ___ when a condition is rare:
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5Bayes' theorem: P(A|B) = [P(B|A) × P(A)] / .
6For P(A)=0.05, P(B|A)=0.7, P(B)=0.15, P(A|B) = .
7If P(A)=0.05, P(B|A)=0.7, P(B)=0.15, find P(A|B).
8Disease 3%, true-positive 85%, false-positive 10%. Find P(positive test).
9Using the previous result, find P(has disease | tests positive).
🚀 Section C · Challenge ● CHALLENGE 5
10Factory A makes 70% of parts at 1% defect; Factory B makes 30% at 4% defect. Find P(defective).
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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1-A 2-A 3-A 4-B | 5 P(B) 6 0.233 7 = 0.233 8 = 0.1225 9 = 0.208 | 10 = 0.019