4.13 Bayes' theorem

4.13 Bayes' theorem Quiz

IB Maths: Analysis and Approaches HL: Quiz

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  1. 1. P(A)=0.4P(A) = 0.4, P(B∣A)=0.5P(B \mid A) = 0.5 and P(B∣A′)=0.25P(B \mid A') = 0.25. Find P(A∣B)P(A \mid B).

    • A. 47\frac{4}{7}
    • B. 0.50.5
    • C. 0.350.35
    • D. 27\frac{2}{7}

  2. 2. A fair coin decides between bag X (3 red, 2 blue) and bag Y (1 red, 4 blue). One ball is drawn and it is red. Find the probability it came from bag X.

    • A. 35\frac{3}{5}
    • B. 34\frac{3}{4}
    • C. 12\frac{1}{2}
    • D. 310\frac{3}{10}

  3. 3. Suppliers P, Q, R provide 20%, 30%, 50% of parts, with fault rates 10%, 5%, 2%. A part is faulty. Find the probability it came from P.

    • A. 0.10.1
    • B. 0.20.2
    • C. 49\frac{4}{9}
    • D. 0.0450.045

  4. 4. Which expression is the denominator in Bayes' theorem when finding P(B∣A)P(B \mid A) for two events?

    • A. P(B)P(B)
    • B. P(A∣B)P(A \mid B)
    • C. P(A∩B)P(A \cap B)
    • D. P(A)P(A)

  5. 5. 1% of people have a condition. A test is always positive for those who have it and positive for 1% of those who do not. Roughly what is the probability that someone who tests positive has the condition?

    • A. 0.50
    • B. 0.99
    • C. 0.01
    • D. 1

Quiz