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Question Number 148569 by puissant last updated on 29/Jul/21

Commented by Olaf_Thorendsen last updated on 29/Jul/21

$$\mathrm{Remarque}:$$$$\mathrm{Si}x\mathrm{est}\mathrm{le}\mathrm{laps}\mathrm{de}\mathrm{temps}\mathrm{que}\mathrm{les}\mathrm{deux}$$$$\mathrm{amis}\mathrm{acceptent}\mathrm{de}{\mathrm{s}}^{\prime }\mathrm{attendre},\mathrm{la}$$$$\mathrm{formule}\mathrm{generale}\mathrm{est}:$$$$p=1-\frac{{(60-x)}^2}{{60}^2}$$$$\mathrm{Et}\mathrm{la}\mathrm{probabilite}\mathrm{devient}\mathrm{superieure}$$$$\mathrm{a}50\mathrm{\%}\mathrm{quand}x\mathrm{est}\mathrm{superieur}\mathrm{a}$$$$17,573\mathrm{minutes}.$$

Answered by Olaf_Thorendsen last updated on 29/Jul/21

$$‘‘\mathrm{Un}\mathrm{bon}\mathrm{croquis}\mathrm{vaut}\mathrm{mieux}{\mathrm{qu}}^{\prime }\mathrm{un}$$$$\mathrm{long}\mathrm{discours}{.}^{″}$$$$-\mathrm{Napoleon}\mathrm{Bonaparte}$$$$$$$$\mathrm{Comme}\mathrm{il}{\mathrm{s}}^{\prime }\mathrm{agit}\mathrm{de}\mathrm{variables}\mathrm{continues},$$$$\mathrm{on}{\mathrm{s}}^{\prime }\mathrm{en}\mathrm{sort}\mathrm{effectivement}\mathrm{mieux}\mathrm{avec}$$$$\mathrm{avec}\mathrm{un}\mathrm{shema}.$$$$\mathrm{En}\mathrm{abscisses},{\mathrm{c}}^{\prime }\mathrm{est}{\mathrm{l}}^{\prime }\mathrm{heure}{\mathrm{d}}^{\prime }\mathrm{arrivee}$$$${\mathrm{d}}^{\prime }\mathrm{Olaf}.$$$$\mathrm{En}\mathrm{ordonnees},{\mathrm{c}}^{\prime }\mathrm{est}{\mathrm{l}}^{\prime }\mathrm{heure}{\mathrm{d}}^{\prime }\mathrm{arrivee}$$$$\mathrm{de}\mathrm{Puissant}.$$$$\mathrm{Chaque}\mathrm{point}\mathrm{du}\mathrm{carre}\mathrm{est}\mathrm{un}\mathrm{cas}$$$$\mathrm{possible}.$$$$\mathrm{Chaque}\mathrm{point}\mathrm{de}\mathrm{la}‘‘{\mathrm{cravate}}^{″}\mathrm{est}\mathrm{un}$$$$\mathrm{cas}\mathrm{probable}.$$$$\mathrm{La}\mathrm{probabilite}\mathrm{cherchee}\mathrm{est}\mathrm{alors}\mathrm{le}$$$$\mathrm{quotient}\mathrm{des}\mathrm{deux}\mathrm{aires}.$$$$$$$$p=\frac{{60}^2-2\times \frac{1}{2}\times {50}^2}{{60}^2}=1-{\left(\frac{5}{6}\right)}^2$$$$p=\frac{11}{36}\approx 30,56\mathrm{\%}$$

Commented by puissant last updated on 29/Jul/21

$$\mathrm{merci}\mathrm{beaucoup}\mathrm{monsieur}\mathrm{olaf}..$$$${\mathrm{j}}^{\prime }\mathrm{apprecie}\mathrm{beaucoup}\mathrm{votre}\mathrm{travail}..$$$$\mathrm{vraiment}\mathrm{merci}...$$

Answered by Olaf_Thorendsen last updated on 29/Jul/21

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