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Two numbers chosen from a range: probability their difference passes a bound

This type of question, asked 3 times: 31 Jan 2023, 30 Jan 2024, 23 Jan 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    31 Jan 2023

    177
    Let AA be the event that the absolute difference between two randomly chosen real numbers in the sample space [0,60]\lbrack 0,60\rbrack is less than or equal to a . If P(A)=1136P(A) =\frac{11}{36}, then a is equal to

  2. Question 2

    30 Jan 2024

    71
    Two integers xx and yy are chosen with replacement from the set {0,1,2,3,….,10}\mathbf{\{ 0,1,2,3,\ldots.,10\}}. Then the probability that ∣x−y∣>5|x - y| > 5 is:

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  3. Question 3

    23 Jan 2026 S1

    74
    From the first 100 natural numbers, two numbers first a and then b are selected randomly without replacement. If the probability that a−b≥10a - b \geq 10 is mn,gcd(m,n)=1\frac{m}{n},gcd(m,n) = 1, then m+nm + n is equal to ____\_\_\_\_ .