Consider the scenario of a player rolling a regular fair six-sided die repeatedly and, based on its outcome, either adding 1 point to his/her score, subtracting 1 point from his/her score or leaving his/her score unchanged until the score first either reaches 0 points ("loss") or 10 points ("win".)

Clearly describe a set of rules (describing which die outcomes lead to points being added, which outcomes lead to points being subtracted and which outcomes lead to the score remaining unchanged) such that, if the player starts with 5 points, he/she is equally likely to win overall i.e. reach 10 points) and he/she is to lose overall. Describe a different set of rules such that the player's chance of winning overall is unchanged but such that the expected number of rolls until the game ends is different. Would your new rules lead to more expected rolls or fewer expected rolls? Justify your answer.

Explain your example in everyday language, not mathematical notation.

(6 marks plus 30 marks for English Language)

Consider the scenario of a player rolling a regular fair six-sided die repeatedly and, based on its outcome, either adding 1 point to his/her score, subtracting 1 point from his/her score or leaving his/her score unchanged until the score first either reaches 0 points (\"loss\") or 10 points (\"win".) In your own words, clearly describe a set of rules (describing which die outcomes lead to points being added, which outcomes lead to points being subtracted and which outcomes lead to the score remaining unchanged) such that, if the player starts with 5 points, he/she is equally likely to win overall i.e. reach 10 points) and he/she is to lose overall. Describe a different set of rules such that the player's chance of winning overall is unchanged but such that the expected number of rolls until the game ends is different. Would your new rules lead to more expected rolls or fewer expected rolls? Justify your answer. Explain your example in everyday language, not mathematical notation. (6 marks plus 30 marks for English Language)