Probability help! Die & bag of blocks!

Question

Noreen is playing a game that has a bag containing two wooden blocks where one is yellow the other is green. to play the game she rolls and eight sided die, if a 12367 or 8 is rolled, she blindly chooses a block from the bag - otherwise she does not get to choose a block. each turn consists of rolling a die a drawing of a block if allowed, returning the block to the bag if it is not green. The game continues until she gets a green block.  What is the probability that the game ends on either Noreen's first or second turn?

Answer 1

 

 1st turn:   3/4*1/2 = 3/8

 

 2nd turn: 1/4 * 3/4* 1/2 = 3/32

 

 3/8 + 3/32 = 12/32 + 3/32 = 15/32