\documentclass[12pt]{article}
\usepackage{amsmath, amssymb, graphicx, array, fancyhdr, unicode-math, multirow}

\DeclareMathOperator{\Var}{Var}
\DeclareMathOperator{\sd}{SD}
\DeclareMathOperator{\Pois}{Pois}
\DeclareMathOperator{\Bin}{Bin}
\DeclareMathOperator{\NegBin}{NegBin}
\DeclareMathOperator{\sech}{sech}


% Text: Calibri, all bold
\setmainfont{Calibri}
\renewcommand{\seriesdefault}{b}

% Math: choose a math font and visually embolden it
\setmathfont{TeX Gyre Termes Math}                  % base math font
\setmathfont[FakeBold=1.9]{TeX Gyre Termes Math}    % embolden; adjust 1.6–2.4

% header
\pagestyle{fancy}
\fancyhf{}
\lhead{\resizebox{!}{2cm}{O}}
\chead{\raisebox{0.5cm}{\Huge Bernoulli Trials}} % (add title text if you want)
\rhead{\resizebox{!}{2cm}{O}}
\setlength{\headheight}{2.5cm}
\setlength{\headsep}{12pt} % space between header and body

\begin{document}
\thispagestyle{fancy}

% -------- PAGE 1 --------
\begin{table}[h!]
  \renewcommand{\arraystretch}{1.2}

% -------- Single -------------------
\begin{tabular}{m{1.2in} m{4in}}
\multirow{5}{*}{\fbox{\includegraphics[width=1in]{images/single.png}}} 
&$ n = 2 $\\
&$ p = 0.50 $\\
&$ k = 1 $\\
&\\
&\\
\end{tabular}

% -------- Abstract -------------------
\begin{tabular}{m{1.2in} m{4in}}
\multirow{5}{*}{\fbox{\includegraphics[width=1in]{images/abstract.png}}} 
&$ P(X = k) = \binom{n}{k}(p)^k(1-p)^{\,n-k} $\\
&$ P(X = 1) = \binom{2}{1}(0.50)^1(0.50)^{1} $\\
&$ P(X = 1) = 2 \times 0.50 \times 0.50 $\\
&$ P(X = 1) = \boxed{0.50}$\\
&\\
\end{tabular}


% -------- Question -------------------
\begin{tabular}{m{1.2in} m{4in}}
\multirow{5}{*}{\fbox{\includegraphics[width=1in]{images/question.png}}} 
&$n=10$\\
&$p=0.20$\\
&$P(X\ge2)=?$\\
&$E[X]=?$\\
\end{tabular}
\end{table}


% second page
\newpage
\thispagestyle{fancy}
\begin{table}[h!]
% -------- Answer -------------------
\begin{tabular}{m{1.2in} m{4in}}
\multirow{5}{*}{\fbox{\includegraphics[width=1in]{images/key.png}}} 
&$n=10$\\
&$p=0.20$\\
&$P(X\ge2)=?$\\
&$E[X]=?$\\
&\hrule\\
&\\
&$P(X\ge2)=1 - P(X\le1)$\\
&$P(X\ge2)=1 - \bigl[P(X=0)+P(X=1)\bigr]$\\
&$P(X=0)=(0.8)^{10}\approx0.107374$\\
&$P(X=1)=\binom{10}{1}(0.2)(0.8)^9 =10\cdot0.2\cdot0.8^9\approx0.268435$\\
&$P(X\ge2)\approx1 - (0.107374 + 0.268435)\approx\boxed{0.62419}$\\
&\hrule\\
&\\
&$E[X] = n\,p = 10\times0.2 = \boxed{2}$\\
\end{tabular}
\end{table}
\end{document}