An eight- sided die is marked with numbers 1, 2, … , 8. A game is played by rolling the die until an 8 appears on the uppermost face. At this point the game ends.
- Using a tree diagram, or otherwise, explain why the probability of the game ending before the fourth roll is
`qquad qquad 1/8 + 7/8 xx 1/8 + (7/8)^2 xx 1/8`. (2 marks)
--- 8 WORK AREA LINES (style=lined) ---
- What is the smallest value of `n` for which the probability of the game ending before the `n`th roll is more than `3/4`? (3 marks)
--- 6 WORK AREA LINES (style=lined) ---