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1. $$\begin{array}{rlr}P(\mathrm{A}\cap \mathrm{B})& =\frac{2}{7}\times \frac{5}{7}=\frac{10}{49}.& \\ P(\bar{\mathrm{A}}\cap \mathrm{B})& =\frac{3}{5}\times \frac{5}{7}=\frac{3}{7}.& \end{array}$$

2. Donc : $$\begin{array}{rlr}P(\mathrm{B})& =P(\mathrm{A}\cap \mathrm{B})+P(\bar{\mathrm{A}}\cap \mathrm{B})& \\ & =\frac{10}{49}+\frac{3}{7}& \\ & =\frac{10}{49}+\frac{21}{49}& \\ & =\frac{31}{49}.& \end{array}$$

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code : 127006