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

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

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

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