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Conditional probability by counting outcomes in the reduced sample space

This type of question, asked 3 times: May 2021 S1, 25 Apr 2025 S1, 15 May 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    May 2021 S1

    112
    Out of 50 tickets numbered 00, 01, 02, \ldots, 49, one ticket is drawn randomly. The probability of the ticket having the product of its digits 7, given that the sum of the digits is 8, is

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  2. Question 2

    25 Apr 2025 S1

    139
    A family has 3 children. The probability that all the three children are girls, given that at least one of them is a girl is

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  3. Question 3

    15 May 2026 S1

    100
    Two fair dice are tossed simultaneously. Let AA be the event that the sum of the numbers is prime, and BB be the event that at least one die shows a number 5. The odds against the occurrence of event BB given that event AA has already occurred is:

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