Question

CQ (5 points) table below, only one among the proposed answers to each question is correct. the number of each \begin{tabular}{|l|l|l|l|} \hline \multirow{2}{}{Questions} & \multicolumn{3}{|c|}{\multirow{2}{}{}} \\ \hline The domain of definition of the function \( f \) given by & a & Proposed answers & c \\ \hline \( \mathrm{f}(\mathrm{x})=\ln \left(\mathrm{e}^{\mathrm{x}+1}-1\right) \) is & ]0, + \( \infty \) [ & ]-1, + \( \infty \) [ & ]-m, -1] \\ \hline \( \lim _{x \rightarrow 0^{+}} x(1+\ln x)= \) & \( -\infty \) & 0 & 1 \\ \hline Consider the function \( f \) defined over \( ]-\infty,+\infty[ \) as \( f(x)=(x+2) e^{-x+1}-x-1 \) and denote by \( (C) \) its representative curve in an orthonormal system. An equation of the asymptote (d) to (C) at \( +\infty \) is & \( \mathrm{y}=\mathrm{x}+2 \) & \( \mathrm{y}=\mathrm{x}+1 \) & \( \mathrm{y}=-\mathrm{x}-1 \) \\ \hline An urn contains 2 red balls and 5 black balls. Three balls are selected randomly and successively with replacement. The number of different ways of selecting at least 1 red ball is & 25 & 150 & 218 \\ \hline A and B are two independent events of the same universe \( \Omega \) such that \( \mathrm{A} \neq \varnothing \) and \( \mathrm{P}(\mathrm{B})=0.4 \). Then, \( \mathrm{P}(\overline{\mathrm{B}} / \mathrm{A})= \) & 0.4 & 0.5 & 0.6 \\ \hline \end{tabular} robability (5 points) A ider two urns U and V . contains 3 red balls and 5 black balls. contains 7 red balls and 2 black balls. of the two urns U and V is randomly chosen and then, 2 balls are selected randomly and simultaneo the chosen urn. sider the following events: "The chosen urn is \( U \) ", "The two selected balls have different colors". a) Calculate the probabilities \( \mathrm{P}(\mathrm{D} / \mathrm{U}) \) and \( \mathrm{P}(\mathrm{U} \cap \mathrm{D}) \). b) Deduce that \( P(D)=\frac{233}{504} \). Knowing that the two selected balls have the same color, calculate the probability that they ar Calculate \( \mathrm{P}(\mathrm{UUD}) \). urn V. B balls are selected randomly and successively without replacement from um U , and two balls an

          CQ (5 points) table below, only one among the proposed answers to each question is correct. the number of each
\begin{tabular}{|l|l|l|l|}
\hline \multirow{2}{*}{Questions} & \multicolumn{3}{|c|}{\multirow{2}{*}{}} \\
\hline The domain of definition of the function \( f \) given by & a & Proposed answers & c \\
\hline \( \mathrm{f}(\mathrm{x})=\ln \left(\mathrm{e}^{\mathrm{x}+1}-1\right) \) is & ]0, + \( \infty \) [ & ]-1, + \( \infty \) [ & ]-m, -1] \\
\hline \( \lim _{x \rightarrow 0^{+}} x(1+\ln x)= \) & \( -\infty \) & 0 & 1 \\
\hline Consider the function \( f \) defined over \( ]-\infty,+\infty[ \) as \( f(x)=(x+2) e^{-x+1}-x-1 \) and denote by \( (C) \) its representative curve in an orthonormal system. An equation of the asymptote (d) to (C) at \( +\infty \) is & \( \mathrm{y}=\mathrm{x}+2 \) & \( \mathrm{y}=\mathrm{x}+1 \) & \( \mathrm{y}=-\mathrm{x}-1 \) \\
\hline An urn contains 2 red balls and 5 black balls. Three balls are selected randomly and successively with replacement. The number of different ways of selecting at least 1 red ball is & 25 & 150 & 218 \\
\hline A and B are two independent events of the same universe \( \Omega \) such that \( \mathrm{A} \neq \varnothing \) and \( \mathrm{P}(\mathrm{B})=0.4 \). Then, \( \mathrm{P}(\overline{\mathrm{B}} / \mathrm{A})= \) & 0.4 & 0.5 & 0.6 \\
\hline
\end{tabular}
robability (5 points)
A
ider two urns U and V .
contains 3 red balls and 5 black balls.
contains 7 red balls and 2 black balls.
of the two urns U and V is randomly chosen and then, 2 balls are selected randomly and simultaneo the chosen urn.
sider the following events:
"The chosen urn is \( U \) ",
"The two selected balls have different colors".
a) Calculate the probabilities \( \mathrm{P}(\mathrm{D} / \mathrm{U}) \) and \( \mathrm{P}(\mathrm{U} \cap \mathrm{D}) \).
b) Deduce that \( P(D)=\frac{233}{504} \).

Knowing that the two selected balls have the same color, calculate the probability that they ar
Calculate \( \mathrm{P}(\mathrm{UUD}) \). urn V.
B
balls are selected randomly and successively without replacement from um U , and two balls an

CQ (5 points) table below, only one among the proposed answers to each question is correct. the number of each

2*Questions 3|c|2*

The domain of definition of the function f given by a Proposed answers c

f(x)=ln(e^x+1-1) is ]0, + ∞ [ ]-1, + ∞ [ ]-m, -1]

limx → 0^+ x(1+ln x)= -∞ 0 1

Consider the function f defined over ]-∞,+∞[ as f(x)=(x+2) e^-x+1-x-1 and denote by (C) its representative curve in an orthonormal system. An equation of the asymptote (d) to (C) at +∞ is y=x+2 y=x+1 y=-x-1

An urn contains 2 red balls and 5 black balls. Three balls are selected randomly and successively with replacement. The number of different ways of selecting at least 1 red ball is 25 150 218

A and B are two independent events of the same universe Ω such that A≠∅ and P(B)=0.4. Then, P(B / A)= 0.4 0.5 0.6

robability (5 points)
A
ider two urns U and V .
contains 3 red balls and 5 black balls.
contains 7 red balls and 2 black balls.
of the two urns U and V is randomly chosen and then, 2 balls are selected randomly and simultaneo the chosen urn.
sider the following events:
"The chosen urn is U ",
"The two selected balls have different colors".
a) Calculate the probabilities P(D / U) and P(U∩D).
b) Deduce that P(D)=(233)/(504).

Knowing that the two selected balls have the same color, calculate the probability that they ar
Calculate P(UUD). urn V.
B
balls are selected randomly and successively without replacement from um U , and two balls an

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