Exercice : Exemple 19
On donne l'arbre des probabilités suivant que valent :
Question
\(p(A)\)
Solution
\(p(A)=0,6\)
Question
\(p_A(B)\)
Solution
\(p_A(B)=0,3\)
Question
\(p(\overline{A})\)
Solution
\(p(\overline{A})=1-p(A)=1-0,6=0,4\)
Question
\(p_{\overline{A}}(B)\)
Solution
\(p_{\overline{A}}(B)+p_{\overline{A}}(\overline{B})=1\)
\(\iff p_{\overline{A}}(B)+0,9=1\)
\(\iff p_{\overline{A}}(B)=1-0,9\)
\(\iff p_{\overline{A}}(B)=0,1\)
Question
\(p(A \cap B)\)
Solution
\(p_A(B)=\frac{p(A \cap B)}{p(A)}\)
\(\iff p(A \cap B)=p(A) \times p_A(B)\)
\(\iff p(A \cap B)=0,6 \times 0,3\)
\(\iff p(A \cap B)=0,18\)
Question
\(p(\overline{A} \cap B)\)
Solution
\(p_{\overline{A}}(B)=\frac{p(\overline{A} \cap B)}{p(\overline{A})}\)
\(\iff p(\overline{A} \cap B)=p_{\overline{A}}(B) \times p(\overline{A})\)
\(p(\overline{A} \cap B)=0,1 \times 0,4=0,04\)