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?  Answers
A) 32 / 31  B) 33 / 31  C) 34 / 31  D) 36 / 31  E) 0 / 31
<gadget id="calculator">6 - 1</gadget>
<output>5</output>

<gadget id="calculator">5 / 6</gadget>
<output>5/6 = around 0.833333</output>

<gadget id="calculator">(5/6) / 6</gadget>
<output>5/36 = around 0.138889</output>

<gadget id="calculator">1 - (5/36)</gadget>
<output>31/36 = around 0.861111</output>

<gadget id="calculator">1 / (31/36)</gadget>
<output>36/31 = around 1.16129</output>

<result>D</result>
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?
divide(const_1, subtract(const_1, divide(divide(subtract(6, 1), 6), 6)))
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