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Bag of unknown make-up (all make-ups equally likely): probability of a make-up after a draw

This type of question, asked 3 times: 31 Jan 2023, 1 Feb 2024, 28 Jan 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    31 Jan 2023

    67
    A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least 5 black balls is

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  2. Question 2

    1 Feb 2024

    61
    A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and other 2 balls are black. The probability that the bag contains equal number of white and black balls is:

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  3. Question 3

    28 Jan 2026 S1

    59
    A bag contains 10 balls out of which k are red and (10−k)(10 - k) are black, where 0≤k≤100 \leq k \leq 10. If three balls are drawn at random without replacement and all of them are found to be black, then the probability that the bag contains 1 red and 9 black balls is :

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