Bayes' Theorem

Grade 12 Maths — Bayes' Theorem: 25 practice questions with instant scoring and explanations.

1. Bayes' Theorem states P(A|B) = :
2. For a partition {A₁, A₂, ...}, P(B) = :
3. In medical testing, given P(disease) = 0.01, P(positive|disease) = 0.95, P(positive|no disease) = 0.05, then P(disease|positive) = :
4. Bayes' Theorem updates our belief from:
5. In Bayes' formula, P(A) is called the:
6. P(B|A) in Bayes' formula is called the:
7. P(A|B) in Bayes' formula is called the:
8. P(B) in the denominator of Bayes' is the:
9. A factory produces items; 2% are defective. A test correctly identifies defects 98% of the time. If an item tests positive, P(actually defective) = :
10. In spam filter classification, P(spam|contains 'free') uses Bayes' to find:
11. Three urns contain: A: 2 red, 3 blue; B: 1 red, 4 blue; C: 3 red, 1 blue. If an urn is chosen randomly and a ball drawn is red, P(urn C was chosen | red drawn) = :
12. If P(A|B) = 0.8 and P(B|A) = 0.6 and P(A) = 0.4, then P(B) = :
13. For Bayes' Theorem to apply, the events must form:
14. Bayes' Theorem is used in:
15. If P(B) = Σᵢ P(B|Aᵢ) P(Aᵢ), then P(Aⱼ|B) = :
16. Applying Bayes' multiple times (sequential updates) requires:
17. If P(positive|disease) = 0.99 and P(positive|no disease) = 0.01, with P(disease) = 0.001, then P(disease|positive) ≈ :
18. The denominator in Bayes' formula can be computed as:
19. For diagnostic tests, the positive predictive value (PPV) is:
20. Sensitivity of a test = P(positive | disease) is the:
21. Specificity of a test = P(negative | no disease) is the:
22. Bayes' Theorem relates posterior, likelihood, prior, and evidence because:
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