20 P. 128

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\[ \begin{array}{|c|c|c|c|c|} \hline P(A) & P(B) & P(A\cap B) & P_B(A) & P_A(B) \\ \hline 0,22 & 0,56 & \mathbf{0,196}\ {\scriptstyle (1)} & 0,35 & \mathbf{0,891}\ {\scriptstyle (2)}\\ \hline \mathbf{0,033}\ {\scriptstyle (3)} & 0,80 & 0,02 & \mathbf{0,025}\ {\scriptstyle (4)} & 0,60 \\ \hline \rule[-1em]{0em}{2.8em}\dfrac3{10} & \mathbf{\dfrac{7}{32}}\ {\scriptstyle(6)} & \mathbf{\dfrac 1 8}\ {\scriptstyle(5)}& \dfrac 47 & \dfrac5{12} \\ \hline \rule[-1em]{0em}{2.8em}\mathbf{\dfrac13}\ {\scriptstyle(8)} & \dfrac 25& \mathbf{\dfrac27}\ {\scriptstyle(7)}& \dfrac57& \dfrac67 \\ \hline \end{array} \]

Calculs :
(1)$P(A\cap B) = P(B)\times P_B(A) = 0,56 \times 0,35 = 0,196$;
(2) $P_A(B) = \dfrac{P(A\cap B)}{P(A)} = \dfrac{0,196}{0,22}\approx 0,891$;
(3) $\small P_A(B) = \dfrac{P(A\cap B)}{P(A)} \iff P(A) = \dfrac{P(A\cap B)}{P_A(B)} = \dfrac{0,02}{0,60} \approx 0,033$;
(4) $P_B(A) = \dfrac{P(A\cap B)}{P(B)} = \dfrac{0,02}{0,80} = 0,025$;
(5) $P(A\cap B) = P(A)\times P_A(B) = \dfrac3{10}\times\dfrac{5}{12} = \dfrac18$;
(6) $\small P_B(A) = \dfrac{P(A\cap B)}{P(B)} \iff P(B) = \dfrac{P(A\cap B)}{P_B(A)} = \dfrac{1/8}{4/7} = \dfrac7{32}$;
(7) $P(A\cap B) = P(B)\times P_B(A) = \dfrac25\times\dfrac57 = \dfrac27$;
(8) $P_A(B) = \dfrac{P(A\cap B)}{P(A)} \iff P(A) = \dfrac{P(A\cap B)}{P_A(B)} = \dfrac{2/7}{6/7} = \dfrac 1 3$.

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code : 128020