6 P. 127

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1. \[\begin{aligned} P(\mathrm A\cap \mathrm B) &= \frac 2 7 \times \frac 5 7 = \frac{10}{49}.& \\ P(\overline{\mathrm A}\cap \mathrm B)&= \frac 3 5 \times \frac 5 7 = \frac{3}{7}.& \end{aligned}\]

2. Donc : \[\begin{aligned} P(\mathrm B) &= P(\mathrm A\cap \mathrm B) + P(\overline{\mathrm A}\cap \mathrm B)& \\ &= \frac{10}{49} + \frac{3}{7}& \\ &=\frac{10}{49}+\frac{21}{49}& \\ &=\frac{31}{49}.& \end{aligned}\]

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code : 127006