In the left scope, how to automate evenly distributing the red circles along the third blue circle instead of manually drawing and shifting them; and making this third circle invisible (white).

In the right scope, how to gather the red circles around a certain point and control the distances between them to make the second and third drawings.

documentclass{beamer}

beamertemplatenavigationsymbolsempty

usepackage{tikz}

begin{document}

begin{frame}[t]

frametitle{bias}

begin{minipage}{textwidth}

{

tikzset{pics/.cd,cc/.style={code={draw [red, thin, fill=red] circle (0.248cm);}}}

begin{tikzpicture}[scale=.9, transform shape]

begin{scope}[scale=.4]

draw[black, thick, fill=black] (0,0)node (o){} circle (0.24cm);

draw[black, thick, dashdotted] ([shift={(-90.:5.4cm)}]o.center) -- ([shift={(90.:5.4cm)}]o.center) ([shift={(180.:5.4cm)}]o.center) -- ([shift={(0.:5.4cm)}]o.center);

foreach r in {1, 2,2.5,3,4,5} draw[blue, thick] (o.center) circle (r);

pic at ([shift={(-90.:2.4cm)}]o.center) {cc};

pic at ([shift={(90.:2.4cm)}]o.center) {cc};

pic at ([shift={(170.:2.48cm)}]o.center) {cc};

pic at ([shift={(10.:2.48cm)}]o.center) {cc};

pic at ([shift={(45.:2.48cm)}]o.center) {cc};

pic at ([shift={(-45.:2.48cm)}]o.center) {cc};

pic at ([shift={(135.:2.48cm)}]o.center) {cc};

pic at ([shift={(-135.:2.48cm)}]o.center) {cc};

end{scope}

begin{scope}[scale=.4, xshift=14cm]

draw[black, thick, fill=black] (0,0)node (o){} circle (0.24cm);

draw[black, thick, dashdotted] ([shift={(-90.:5.4cm)}]o.center) -- ([shift={(90.:5.4cm)}]o.center) ([shift={(180.:5.4cm)}]o.center) -- ([shift={(0.:5.4cm)}]o.center);

foreach r in {1, 2,...,5} draw[blue, thick] (o.center) circle (r);

pic at ([shift={(145.:2.48cm)}]o.center) {cc};

pic at ([shift={(156.:2.4cm)}]o.center) {cc};

pic at ([shift={(145.:3.cm)}]o.center) {cc};

pic at ([shift={(150.:3.6cm)}]o.center) {cc};

 pic at ([shift={(159.:3.6cm)}]o.center) {cc};

pic at ([shift={(168.:2.48cm)}]o.center) {cc};

pic at ([shift={(168.:3.6cm)}]o.center) {cc};

pic at ([shift={(168.:3.06cm)}]o.center) {cc};

end{scope}

end{tikzpicture}

}

end{minipage}

end{frame}

end{document}

Is this what you are lookig for?

documentclass[border=3mm]{standalone}

usepackage{tikz}

begin{document}

tikzset{pics/.cd,cc/.style={code={draw [black, thin, fill=red] circle (0.248cm);}}}

begin{tikzpicture}[scale=.9, transform shape]

begin{scope}[scale=.4]

draw[black, thick, fill=black] (0,0)node (o){} circle (0.24cm);

draw[black, thick, dashdotted] ([shift={(-90.:5.4cm)}]o.center) -- ([shift={(90.:5.4cm)}]o.center) ([shift={(180.:5.4cm)}]o.center) -- ([shift={(0.:5.4cm)}]o.center);

foreach r in {1, 2,3,4,5} draw[blue, thick] (o.center) circle (r);

foreach ang in {0,45,...,315}

    pic at (ang:2.5cm) {cc};

end{scope}

begin{scope}[scale=.4, xshift=14cm]

draw[black, thick, fill=black] (0,0)node (o){} circle (0.24cm);

draw[black, thick, dashdotted] ([shift={(-90.:5.4cm)}]o.center) -- ([shift={(90.:5.4cm)}]o.center) ([shift={(180.:5.4cm)}]o.center) -- ([shift={(0.:5.4cm)}]o.center);

foreach r in {1, 2,...,5} draw[blue, thick] (o.center) circle (r);

defdist{0.7}

coordinate (p) at (240:3cm);

foreach ang in {0,45,...,315}

    pic at ([shift={(ang:dist)}]p) {cc};

end{scope}

end{tikzpicture}

end{document}

A PSTricks solution only for comparison purposes.

One

documentclass[pstricks,border=12pt]{standalone}

pstVerb{realtime srand}

begin{document}

begin{pspicture}(-6,-6)(6,6)

    qdisk(0,0){5pt}

    foreach i in {1,...,6}{pscircle[linecolor=blue]{i}}

    foreach i in {0,1,...,7}{pscircle[fillstyle=solid,fillcolor=red,origin={!3 45 ispace mul PtoC}]{5pt}}

    psset{linestyle=dashed}    

    psline(0,-6)(0,6)

    psline(-6,0)(6,0)

end{pspicture}

end{document}

Two

documentclass[pstricks,border=12pt]{standalone}

pstVerb{realtime srand}

begin{document}

begin{pspicture}(-6,-6)(6,6)

    qdisk(0,0){5pt}

    foreach i in {1,...,6}{pscircle[linecolor=blue]{i}}

    psLoop{8}{pscircle[fillstyle=solid,fillcolor=red,origin={-3,-2}](!Rand .5 mul Rand 360 mul PtoC){5pt}}

    psset{linestyle=dashed}    

    psline(0,-6)(0,6)

    psline(-6,0)(6,0)

end{pspicture}

end{document}

Three

documentclass[pstricks,border=12pt]{standalone}

pstVerb{realtime srand}

begin{document}

begin{pspicture}(-6,-6)(6,6)

    qdisk(0,0){5pt}

    foreach i in {1,...,6}{pscircle[linecolor=blue]{i}}

    foreach i in {0,1,...,7}{pscircle[fillstyle=solid,fillcolor=red,origin={3;225}](!.5 45 ispace mul PtoC){5pt}}

    psset{linestyle=dashed}    

    psline(0,-6)(0,6)

    psline(-6,0)(6,0)

end{pspicture}

end{document}