Binomial distribution with decimal places in x axis?

You need to define the interval width in the samples at key. E.g. samples at={0.0,0.01,...,1.0}.

\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}

\begin{document}

\begin{tikzpicture}[
    declare function={binom(\k,\n,\p)=\n!/(\k!*(\n-\k)!)*\p^\k*(1-\p)^(\n-\k);}
]
    \begin{axis}[
        width=\textwidth,
        height=\axisdefaultheight,
        samples at={0.0,0.01,...,1.0},
        yticklabel style={
            /pgf/number format/fixed,
            /pgf/number format/fixed zerofill,
            /pgf/number format/precision=1
        }
    ]
        \addplot [only marks, orange] {binom(11,30,x)}; 
    \end{axis}
\end{tikzpicture}

\end{document}

Edit

I added the lines under each marker using a bar chart with bars of zero width.

\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}

\begin{document}

\begin{tikzpicture}[
    declare function={binom(\k,\n,\p)=\n!/(\k!*(\n-\k)!)*\p^\k*(1-\p)^(\n-\k);}
]
    \begin{axis}[
        width = \textwidth,
        height = \axisdefaultheight,
        title style = {align = center},
        title = {Multiple Binomial Distributions \\ for $k=11$, $n=30$},
        xlabel = {$p$},
        ylabel = {probability of $k$ given $p$},
        samples at = {0.0,0.01,...,1.0},
        tick pos = lower,
        tick align = outside,
        every tick/.style = {black},
        yticklabel style={
            /pgf/number format/fixed,
            /pgf/number format/fixed zerofill,
            /pgf/number format/precision=1
        }
    ]
        \addplot [
            ybar,
            bar width = 0pt,
            mark = *,
            mark options = {
                blue
            },
            mark size = 1pt,
            red
        ]
            {binom(11,30,x)}; 
    \end{axis}
\end{tikzpicture}

\end{document}

Your diagram can also be drawn as follows:

• define domain: domain=0:1,
• define number of samples, for example: samples=100,
• use ycomb option (diagram will become similar to showed in question},
• slightly restyle axis options:

\documentclass[margin=2mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}

\begin{document}
    \begin{tikzpicture}[%
declare function={binom(\k,\n,\p)=\n!/(\k!*(\n-\k)!)*\p^\k*(1-\p)^(\n-\k);}
                        ]
\begin{axis}[
    width=\textwidth, height=\axisdefaultheight,
    font=\sffamily,
    ylabel={probability of $k$ given $p$},
    xlabel={$p$},
    xmax=1,
    enlarge x limits=0.05,
    tick label style={/pgf/number format/assume math mode=true, 
                      font=\footnotesize\sffamily},
    yticklabel style={/pgf/number format/.cd, fixed,
                      fixed zerofill, precision=2},
        domain=0:1,samples=100,
    mark options={scale=0.75, blue},
        ]
\addplot +[ycomb,draw=orange] {binom(11,30,x)};
\end{axis}
    \end{tikzpicture}
\end{document}