Question

SUBIECTUL al III-lea.
Exercitiul 1!!!


Puteti rezolva si doar punctul a daca vreti

Answer 1

Notăm datele să le vedem mai bine.

a- bile albe

r- bile rosii

n- bile negre

x- nr total de bile

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$a) \: \: a = \tfrac{7x}{12} \\ \\ n = 40\%\cdot(x - \tfrac{7x}{12} ) \\ n= \tfrac{40}{100} \cdot \tfrac{5x}{12} \\ n= \tfrac{1}{2} \cdot \tfrac{x}{3} \\ n = \tfrac{x}{6} \\ \\ r = 60\%\cdot(x - \tfrac{7x}{12} ) \\ r= \tfrac{60}{100} \cdot \tfrac{5x}{12} \\ r = \tfrac{5x}{20} \\r = \tfrac{x}{4} \\ \\ \sout{ - - - - - - - - - - - - - - - -} \\ r = n + 12 \\ \\ \frac{x}{4} = \frac{x}{6} + 12 \\ \\ \frac{3x}{12} = \frac{2x}{12} + \frac{144}{12} \\ 3x = 2x + 144 \\ x = 144 \\\underline{\large\text{acum \: inlocuim \: x : } }\\ \\ a = \tfrac{7 \times 144}{12} = \color{green}84\text{(bile \: albe)} \\ n = \tfrac{144}{6} =\color{lime} 24\text{(bile \: negre)} \\ r = \frac{144}{4} = \color{olive}36\text{(bile \: rosii)} \\ \sout{ - - - - - - - - - - - - - - - - }\\\sout{ - - - - - - - - - - - - - - - - }\\ b) \: \tt{probablitatea = } \frac{24 + 84}{24 + 84 + 36} \\ \\ \tt{probabilitatea = } \frac{108}{144} \\ \\\boxed{ \tt{probabilitatea = }0.75\%}$