6 The probability that Sue completes a Sudoku puzzle correctly is 0.75 .
- Sue attempts \(n\) Sudoku puzzles. Find the least value of \(n\) for which the probability that she completes all \(n\) puzzles correctly is less than 0.06 .
Sue attempts 14 Sudoku puzzles every month. The number that she completes successfully is denoted by \(X\).
- Find the value of \(X\) that has the highest probability. You may assume that this value is one of the two values closest to the mean of \(X\).
- Find the probability that in exactly 3 of the next 5 months Sue completes more than 11 Sudoku puzzles correctly.