let-x-y-z-be-random-numbers-from-0-to-10-where-x-y-z-R-what-is-the-probability-that-a-all-the-following-is-satisfied-x-y-2-x-z-2-y-z-2-b-the-probability-that-one-or-two-of-them-are-not-sat

Question Number 205409 by Red1ight last updated on 20/Mar/24

$$\mathrm{let}\:{x},\:{y},\:{z}\:\mathrm{be}\:\mathrm{random}\:\mathrm{numbers}\:\mathrm{from}\:\mathrm{0}\:\mathrm{to}\:\mathrm{10} \\ $$$$\mathrm{where}\:{x},{y},{z}\in\mathbb{R} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\left.{a}\right)\:\mathrm{all}\:\mathrm{the}\:\mathrm{following}\:\mathrm{is}\:\mathrm{satisfied} \\ $$$$\mid{x}−{y}\mid\geqslant\mathrm{2} \\ $$$$\mid{x}−{z}\mid\geqslant\mathrm{2} \\ $$$$\mid{y}−{z}\mid\geqslant\mathrm{2} \\ $$$$\left.{b}\right)\:\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\:\mathrm{one}\:\mathrm{or}\:\mathrm{two}\:\mathrm{of}\:\mathrm{them}\:\mathrm{are}\:\mathrm{not}\:\mathrm{satisfied} \\ $$$$\left.{c}\right)\:\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{all}\:\mathrm{of}\:\mathrm{them}\:\mathrm{are}\:\mathrm{not}\:\mathrm{satisfied} \\ $$$$ \\ $$

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