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? Choose the correct answer.
A) 32/31 B) 33/31 C) 34/31 D) 36/31 E) 0/31
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= 
<gadget id="calculator"> 1/6 *6</gadget>
<output>1</output>
1 and   common ratio 5/6* 1/6= 5/36 . Hence, Connie's expected earnings are   1/1- 5/36   =   36/31   correct answer 36/31
<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?