The Biggest Loser

Question

Fred is playing a game that costs $\$1$ to play per round. He has a probability $0 < p < 1$ of winning each round. If Fred wins a given round, he receives an integer amount $\$k > 1$ (note that he does not receive the $\$1$ initially paid back). If Fred initially starts with an integer amount $\$s \geq 1$ in his bank, find the probability that Fred wins exactly once before going bankrupt when $s = 3, k = 4,$ and $p = 1/3$. Round to the nearest ten-thousandth.