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Questions: Algebra BusinessCalculus
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A bag contains 3 green marbles, and 2 blue marbles. If 2 marbles are selected, what is the probability of picking 2 green marbles?
There are \(\displaystyle C(5,2)=10\) to select 2 marbles. There are \(\displaystyle 3\) ways to select 2 green from 3 green. This gives the probability \(\displaystyle \frac{3}{10}\)
\begin{question}A bag contains 3 green marbles, and 2 blue marbles. If 2 marbles are selected, what is the probability of picking 2 green marbles? \soln{9cm}{There are $C(5,2)=10$ to select 2 marbles. There are $3$ ways to select 2 green from 3 green. This gives the probability $\frac{3}{10}$} \end{question}
\documentclass{article} \usepackage{tikz} \usepackage{amsmath} \usepackage[margin=2cm]{geometry} \usepackage{tcolorbox} \newcounter{ExamNumber} \newcounter{questioncount} \stepcounter{questioncount} \newenvironment{question}{{\noindent\bfseries Question \arabic{questioncount}.}}{\stepcounter{questioncount}} \renewcommand{\labelenumi}{{\bfseries (\alph{enumi})}} \newif\ifShowSolution \newcommand{\soln}[2]{% \ifShowSolution% \noindent\begin{tcolorbox}[colframe=blue,title=Solution]#2\end{tcolorbox}\else% \vspace{#1}% \fi% }% \newcommand{\hideifShowSolution}[1]{% \ifShowSolution% % \else% #1% \fi% }% \everymath{\displaystyle} \ShowSolutiontrue \begin{document}\begin{question}(10pts) The question goes here! \soln{9cm}{The solution goes here.} \end{question}\end{document}
<p> <p>A bag contains 3 green marbles, and 2 blue marbles. If 2 marbles are selected, what is the probability of picking 2 green marbles?</p> </p>
<p> <p>There are <img class="equation_image" title=" \displaystyle C(5,2)=10 " src="/equation_images/%20%5Cdisplaystyle%20C%285%2C2%29%3D10%20" alt="LaTeX: \displaystyle C(5,2)=10 " data-equation-content=" \displaystyle C(5,2)=10 " /> to select 2 marbles. There are <img class="equation_image" title=" \displaystyle 3 " src="/equation_images/%20%5Cdisplaystyle%203%20" alt="LaTeX: \displaystyle 3 " data-equation-content=" \displaystyle 3 " /> ways to select 2 green from 3 green. This gives the probability <img class="equation_image" title=" \displaystyle \frac{3}{10} " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7B3%7D%7B10%7D%20" alt="LaTeX: \displaystyle \frac{3}{10} " data-equation-content=" \displaystyle \frac{3}{10} " /> </p> </p>