Bonjour Meheriohere,
1) Arbre pondéré en pièce jointe.
[tex]2)a)\ P(\overline{S}\ et\ A)=P_{\bar{S}}(A)\times P(\overline{S})\\\\P(\overline{S}\ et\ A)=0,96\times0,05[/tex]
[tex]\boxed{P(\overline{S}\ et\ A)=0,048=4,8\ \%}[/tex]
[tex]b)\ P(S\ et\ A)=P_{S}(A)\times P(S})\\\\P(S\ et\ A)=0,02\times0,95[/tex]
[tex]\boxed{P(S\ et\ A)=0,019=1,9\ \%}[/tex]
[tex]c)\ P(A)=P[(\overline{S}\ et\ A)\ ou\ (S\ et\ A)]\\\\P(A)=P(\overline{S}\ et\ A)+P(S\ et\ A)[/tex]
[tex]P(A)=0,048+0,019\\\\\boxed{P(A)=0,067=6,7\ \%}[/tex]
[tex]3)\ P_A(S)=\dfrac{P(S\ et\ A)}{P(A)}\\\\[/tex]
[tex]P_A(S)=\dfrac{0,019}{0,067}[/tex]
[tex]\boxed{P_A(S)\approx0,28}\\\\\boxed{P_A(S)\approx 28\ \%}[/tex]
