2019 DHS P2 Q11

At a funfair, Alice pays \(\$3\) to play a game by tossing a fair dice until she gets a ‘\(6\)’. Let \(X\) be the number of times that the player tosses a fair dice until he gets a ‘\(6\)’. The prize, \(S\) (in dollars), that the player may win is given by the following function:

\(S=\left\{ \begin{matrix}8, \\4, \\0, \end{matrix} \right.\mathrm{ }\begin{matrix}\mathrm{if }X=1, \\\mathrm{ if }2\le X\le k, \\\mathrm{ otherwise}\mathrm{.} \end{matrix}\)

where \(k\) is a positive integer.