A die has shown a ‘6’ exactly 14 times in 80 rolls.
a. (i) What is the minimum number of additional rolls that must show a ‘6’ so that the empirical probability of getting a ‘6’ reaches at least 0.25?
b. (ii) The player is allowed at most 20 more rolls in total. Can the empirical probability of getting a ‘6’ be raised to 0.30 within this limit? Justify your answer with calculation.