An experiment consists of rolling a die until a 2 appears.How many elements of the sample space correspond to the event that the 2 appears not later than the $k^{th}$ roll of the die?[Hint (a) first (k-1) rolls have 5 outcomes each and $k^{th}$ rolls should result in 1 outcomes.(b) $1+5+5^2+.......5^{k-1}$]

Question

$\begin{array}{1 1}(A)\;\large\frac{5^{k-1}}{4}\\(B)\;5^{k+1}\\(C)\;5^k\\(D)\;\text{None of these}\end{array}$