Problem: one day , connie plays a game with a fair 6 - sided die . connie rolls the die until she rolls a 6 , at which point the game ends . if she rolls a 6 on her first turn , connie wins 6 dollars . for each subsequent turn , connie wins 1 6 of the amount she would have won the previous turn . what is connie ' s expected earnings from the game ?
Rationale: connie has a 1 6 chance of winning 6 dollars her first turn . she has a 5 / 6 1 / 6 chance of winning 1 dollar her second turn . next , she has a 25 36 1 / 6 chance of winning 1 / 6 dollars her third turn . generalizing , connie ' s expected earnings form a geometric series with initial term 1 / 6 * 6 = 1 and common ratio 5 / 6 * 1 / 6 = 5 / 36 . hence , connie ' s expected earnings are 1 / 1 - 5 / 36 = 36 / 31 correct answer d
annotated_formula: divide(const_1, subtract(const_1, divide(divide(subtract(6, 1), 6), 6)))