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Candidate given many problems: probability of failing to solve at most (or fewer than) two

The same question, asked 2 times: 4 May 2023 S2*, 14 May 2024 S1. Every wording below, oldest first.

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  1. Question 1

    4 May 2023 S2

    149
    For an entry to a certain course, a candidate is given twenty problems to solve. If the probability that the candidate can solve any problem is 37\frac{3}{7}, then the probability that he is unable to solve at most two problems is

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  2. Question 2

    14 May 2024 S1

    138
    For an initial screening of an entrance exam, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is 45\dfrac{4}{5}, then the probability that he is unable to solve less than two problems, is

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