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Bayes' theorem: probability of the cause given the observed result

This type of question, asked 8 times: 20 Apr 2025 S2, 23 Apr 2025 S1, 25 Apr 2025 S2, 13 Apr 2026 S2, 16 Apr 2026 S2, 18 Apr 2026 S2, 20 Apr 2026 S1, 12 May 2026 S2. All 8 questions below, oldest first.

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  1. Question 1

    20 Apr 2025 S2

    144
    For k=1,2,3k = 1,2,3 the box BkB_{k} contains k red balls and (k+1)(k + 1) white balls. Let P(B1)=12,P(B2)=13P\left( B_{1} \right)=\frac{1}{2},P\left( B_{2} \right)=\frac{1}{3} and P(B3)=16.AP\left( B_{3} \right)=\frac{1}{6}.A box is selected at random and a ball is drawn from it. If a red ball is drawn from it, then the probability that it comes from box B2B_{2} is

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  2. Question 2

    23 Apr 2025 S1

    147
    Bag I contain 3 red and 2 green balls and Bag II contains 5 red and 3 green balls. A ball is drawn from one of the bag at random and it is found to be green. Then the probability that it is drawn from Bag I is

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  3. Question 3

    25 Apr 2025 S2

    102
    A doctor assumes that patient has one of three diseases d1, d2 or d3. Before any test he assumes an equal probability for each disease. He carries out a test that will be positive with probability 0.7 if the patient has disease d1,0.5d1,0.5 if the patient has disease d 2 and 0.8 if the patient has disease d3. Given that the outcome of the test was positive then probability that patient has disease d2 is

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  4. Question 4

    13 Apr 2026 S2

    100
    A certain disease has a prevalence of 1%1\% in the population. A diagnostic test for the disease has a sensitivity of 98%98\% and a specificity of 95%95\%. If a person from this population tests positive, then the probability that they actually have the disease is...

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  5. Question 5

    16 Apr 2026 S2

    100
    If E1E_1 and E2E_2 are equally likely, mutually exclusive and exhaustive events and P(A∣E1)=0.2P(A|E_1) = 0.2, P(A∣E2)=0.3P(A|E_2) = 0.3, then P(E1∣A)P(E_1|A) equal to...

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  6. Question 6

    18 Apr 2026 S2

    100
    In an entrance test, there are multiple choice questions. There are four possible answers to each question, only one of which is correct. The probability that a student knows the answer to a question is 90%. If he gets the correct answer to a question, then the probability that he was guessing is

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  7. Question 7

    20 Apr 2026 S1

    100
    In a certain city, the ratio of men to women is 5:45 : 4. It is found that 80%80\% of men and 90%90\% of women are literate. If a person selected at random is found to be illiterate, then the probability that the person is a man is....

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  8. Question 8

    12 May 2026 S2

    100
    A man is known to speak the truth in 75%75\% of cases. If he throws an unbiased die and tells his friend that it is a six. Assuming that when he tells a lie, he specifically reports the result as a six, the probability that it is actually a six is...

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