Just doing some practice probability questions and came across this which confused me:

Two darts players

Two darts players

A and B throw alternately at a board and the

1st to score a bull wins the game. The outcomes of different throws are independent and on each throw A has probability pA of scoring a bull while B has probability pB of scoring a bull. If A has the 1st throw, calculate the probability that A wins the game.

1st to score a bull wins the game. The outcomes of different throws are independent and on each throw A has probability pA of scoring a bull while B has probability pB of scoring a bull. If A has the 1st throw, calculate the probability that A wins the game.

I'm not sure what type of question this is (though i would guess at geometric). I'm not sure how to work this out as there is no information about the number of throws and I'm also unsure about how to bring independence into this.

Any advice would be welcome