[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

Let [math]R_i[/math] be the event that the [math]i[/math]th player in a poker game has a

royal flush. Show that a royal flush (A,K,Q,J,10 of one suit) attracts another royal flush, that is [math]P(R_2|R_1) \gt P(R_2)[/math]. Show that a royal flush repels full houses.