\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}{N}}
\chead{\raisebox{0.5cm}{\Huge Posterior Probablities}} % (add title text if you want)
\rhead{\resizebox{!}{2cm}{N}}
\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}}} 
&$ P(H) = 0.30 $\\
&$ P(L) = 0.70 $\\
&$ P(A|H) = 0.40 $\\
&$ P(A|L) = 0.20 $\\
&\\
\end{tabular}


% -------- Abstract -------------------
\begin{tabular}{m{1.2in} m{4in}}
\multirow{5}{*}{\fbox{\includegraphics[width=1in]{images/abstract.png}}} 
&$ P(A) = P(A|H)P(H) + P(A|L)P(L)$\\ 
&$ P(A) = (0.4)(0.3) + (0.2)(0.7) = 0.12 + 0.14 = 0.26   $\\
&\hrule\\
&\\
&$ P(H|A) = \frac{P(A|H)P(H)}{P(A)} = \frac{(0.4)(0.3)}{0.26} = \frac{0.12}{0.26} = \frac{6}{13} \approx 0.4615$\\
&\\
\end{tabular}


% -------- Question -------------------
\begin{tabular}{m{1.2in} m{4in}}
\multirow{5}{*}{\fbox{\includegraphics[width=1in]{images/question.png}}} 
&$P(A) = 0.25$\\
&$P(B) = 0.35 $\\
&$P(C) = 0.40$\\
&$P(D|A) = 0.05$\\ 
&$P(D|B) = 0.04 $\\
&$P(D|C) = 0.02 $\\
&$P(A|D) = ? $\\
\end{tabular}
\end{table}
% second page
\newpage
\thispagestyle{fancy}
\begin{table}[h!]
% -------- Answer -------------------
\begin{tabular}{m{1.2in} m{4in}}
\multirow{5}{*}{\fbox{\includegraphics[width=1in]{images/key.png}}} 
&$P(A) = 0.25$\\
&$P(B) = 0.35 $\\
&$P(C) = 0.40$\\
&$P(D|A) = 0.05$\\ 
&$P(D|B) = 0.04 $\\
&$P(D|C) = 0.02 $\\
&$P(A|D) = ? $\\
&\hrule\\
&\\
&$P(D) = P(D|A)P(A) + P(D|B)P(B) + P(D|C)P(C)$ \\
&$= (0.05)(0.25) + (0.04)(0.35) + (0.02)(0.40) $\\
&$= 0.03$\\
&\hrule\\
&\\
&$ P(A|D)  = \frac{ P(D|A) P(A)}{P(D)}= \frac{(0.03)(0.25)}{0.03} = 0.36$\\

\end{tabular}
\end{table}





\end{document}