TeX inserts breakpoints after binary and relational operators with penalties \binoppenalty
and \relpenalty
. However, subformulas cannot be broken across lines. A pair of curly braces create a subformula as in the example of the question. Therefore the *
does not create a breakpoint.
If you want breakpoints inside the text part of the formula, then the text can be given outside math.
The following example forces line breaks at the breakpoints by putting the examples into a too narrow minipage
:
\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\begin{document}
\begin{minipage}{1mm}
$P^1_{r,s}=\sum\limits_{i=r}^n{P(i\text{ applicant is selected and is the
best})}=\sum\limits_{i=r}^n{P(i\text{ applicant is the best})*P(i\text{ is
selected | is the best})}$.
\end{minipage}
\smallskip\hrule\smallskip
% Remove subformula
\begin{minipage}{1mm}
$P^1_{r,s}=\sum\limits_{i=r}^n{P(i\text{ applicant is selected and is the
best})}=\sum\limits_{i=r}^n{P(i\text{ applicant is the best})}*{P(i\text{ is
selected | is the best})}$.
\end{minipage}
\smallskip\hrule\smallskip
% Text outside math
\begin{minipage}{1mm}
$P^1_{r,s}=\sum\limits_{i=r}^n P(i$ applicant is selected and is
the best$)=\sum\limits_{i=r}^n P(i$ applicant is the best$) * P(i$
is selected | is the best$)$.
\end{minipage}
\end{document}

\text
command