A silent duel with two kinds of weapon

In this paper the silent duel is solved in which Player I has two kinds of weapon, the first with one bullet which he can use when he wants, and the second which he can only when the distance between players is zero. In distinction to the paper of Trybuła (1998), it is assumed here that the probability of success of the second weapon can be smaller than one. Player II has a weapon with one bullet which he can use when he wants.