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Two-numbers-a-and-b-are-chosen-at-random-from-the-set-of-first-30-natural-numbers-The-probability-that-a-2-b-2-is-divisible-by-3-is-




Question Number 111001 by ZiYangLee last updated on 01/Sep/20
Two numbers a and b are chosen at  random from the set of first 30 natural  numbers. The probability that a^2 −b^2   is divisible by 3 is
$$\mathrm{Two}\:\mathrm{numbers}\:{a}\:\mathrm{and}\:{b}\:\mathrm{are}\:\mathrm{chosen}\:\mathrm{at} \\ $$$$\mathrm{random}\:\mathrm{from}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{first}\:\mathrm{30}\:\mathrm{natural} \\ $$$$\mathrm{numbers}.\:\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:{a}^{\mathrm{2}} −{b}^{\mathrm{2}} \\ $$$$\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{3}\:\mathrm{is} \\ $$
Commented by bemath last updated on 01/Sep/20
(5/(29))
$$\frac{\mathrm{5}}{\mathrm{29}} \\ $$

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