Alec and Bill take alternate turns at kicking a football at a goal, and their probabilities of scoring a goal on each kick are 1/3 independently of previous outcomes. The first person to score allows the other person one more kick. If the other then scores, the game is drawn. If the other then misses, the first has won the game. Alec begins a game.
find the expected total number of kicks in the game.

Question

Alec and Bill take alternate turns at kicking a football at a goal, and their probabilities of scoring a goal on each kick are 1/3 independently of previous outcomes. The first person to score allows the other person one more kick. If the other then scores, the game is drawn. If the other then misses, the first has won the game. Alec begins a game. 
find the expected total number of kicks in the game.

anonymous · Answer

a nice challenge for any one wanting to do a probability question and add a series