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Random coefficients chosen from a set: probability a quadratic has real roots

This type of question, asked 2 times: 20 Apr 2025 S1, 19 Apr 2026 S1. All 2 questions below, oldest first.

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  1. Question 1

    20 Apr 2025 S1

    127
    If two numbers pp and qq are chosen randomly from the set {1,2,3,4}\mathbf{\{ 1,2,3,4\}}, one by one, with replacement, then the probability of getting p2≥4qp^{2}\geq 4q is

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  2. Question 2

    19 Apr 2026 S1

    51
    Let aa be an integer selected at random from the set {0,1,2,3,…,9}\{0, 1, 2, 3, \ldots, 9\}. The probability that the equation ax2−ax+1=0ax^2 - ax + 1 = 0 has real roots is ...

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