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Bayes' theorem: one of several bags or sources is chosen; find the probability it was a particular one

This type of question, asked 12 times: 2021 Paper 4, 14 Jun 2022, 25 Jan 2023, 8 Apr 2023, 30 Jan 2024, 4 Apr 2024, 6 Apr 2024, 8 Apr 2024, 28 Jan 2025, 2 Apr 2025, 5 Apr 2026 S1, 8 Apr 2026 S2. All 12 questions below, oldest first.

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  1. Question 1

    2021 Paper 4

    71
    In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are non-smokers and vegetarian. Their chances of getting a particular chest disorder are 35%,20%35\%,20\% and 10%10\% respectively. A person is chosen from the group at random and is found to be suffering from the chest disorder. The probability that the selected person is a smoker and non-vegetarian is:

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  2. Question 2

    14 Jun 2022

    64
    Bag A contains 2 white, 1 black and 3 red balls and bag B contains 3 black, 2 red and nn white balls. One bag is chosen at random and 2 balls drawn from it at random, are found to be 1 red and 1 black. If the probability that both balls come from Bag A is 611\frac{6}{11}, then nn is equal to

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  3. Question 3

    25 Jan 2023

    171
    25%25\% of the population are smokers. A smoker has 27 times more chances to develop lung cancer than a non -smoker. A person is diagnosed with lung cancer and the probability that this person is a smoker is k10\frac{k}{10}. Then the value of kk is.

  4. Question 4

    8 Apr 2023

    68
    In a bolt factory, machines A,BA,B and CC manufacture respectively 20%,30%20\%,30\% and 50%50\% of the total bolts. Of their output 3, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product. If the bolt drawn is found the defective, then the probability that it is manufactured by the machine CC is

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  5. Question 5

    30 Jan 2024

    161
    Bag A contains 3 white, 7 red balls and bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag AA, if the ball drawn in white, is:

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  6. Question 6

    4 Apr 2024

    62
    Three urns A, B and CC contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is selected at random and a ball is drawn from it. If the ball drawn is black, then the probability that it is drawn from urn AA is:

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  7. Question 7

    6 Apr 2024

    70
    A company has two plants AA and BB to manufacture motorcycles. 60%60\% motorcycles are manufactured at plant AA and the remaining are manufactured at plant B. 80%80\% of the motorcycles manufactured at plant A are rated of the standard quality, while 90%90\% of the motorcycles manufactured at plant B are rated of the standard quality. A motorcycle picked up randomly from the total production is found to be of the standard quality. If pp is the probability that it was manufactured at plant BB, then 126 p is

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  8. Question 8

    8 Apr 2024

    165
    There are three bags X,YX,Y and ZZ. Bag XX contains 5 one-rupee coins and 4 five-rupee coins; Bag YY contains 4 one-rupee coins and 5 five-rupee coins and Bag ZZ contains 3 one-rupee coins and 6 five-rupee coins. A bag is selected at random and a coin drawn from it at random is found to be a one-rupee coin. Then the probability, that it came from bag YY, is:

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  9. Question 9

    28 Jan 2025

    126
    Bag B1B_{1} contains 6 white and 4 blue balls, Bag B2B_{2} contains 4 white and 6 blue balls, and BagB3BagB_{3} contains 5 white and 5 blue balls. One of the bags is selected at random and a ball is drawn from it. If the ball is white, then the probability, that the ball is drawn from Bag B2B_{2}, is:

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  10. Question 10

    2 Apr 2025

    135
    Given three identical bags each containing 10 balls, whose colours are as follows :
    BagRedBlueGreen
    Bag I325
    Bag II433
    Bag III514
    A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from bag I is p and if the ball is Green, the probability that it is from bag III is q , then the value of (1p+1q)\left( \frac{1}{p}+\frac{1}{q} \right) is :

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  11. Question 11

    5 Apr 2026 S1

    57
    A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the envelope just two consecutive letters AN are visible. The probability, that the letter came from ANANTPUR, is :

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  12. Question 12

    8 Apr 2026 S2

    56
    A candidate has to go to the examination center to appear in an examination. The candidate uses only one means of transportation for the entire distance out of bus, scooter and car. The probabilities of the candidate going by bus, scooter and car, respectively, are 25,15\frac{2}{5},\frac{1}{5} and 25\frac{2}{5}. The probabilities that the candidate reaches late at the examination center are 15,13\frac{1}{5},\frac{1}{3} and 14\frac{1}{4} if the candidate uses bus, scooter and car, respectively. Given that the candidate reached late at the examination centre, the probability that the candidate travelled by bus is :

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