(i)[3]
Sue works through $n$ Sudoku puzzles. Determine the smallest value of $n$ for which the chance that she gets every one of the $n$ puzzles correct is below $0.06$.
(ii)[3]
Every month Sue attempts $14$ Sudoku puzzles. Let $X$ represent the number she solves correctly. Determine the value of $X$ with the greatest probability. You may assume that this value is one of the two values nearest to the mean of $X$.
(iii)[5]
Find the probability that Sue completes more than $11$ Sudoku puzzles correctly in exactly $3$ of the next $5$ months.