Problem
A gambler makes a sequence of independent bets. In each bet, he wins $1 with probability p, and loses $1 with probability 1-p. Initially, the gambler has $k, and plays until he either accumulates $n or has no money left. What is the probability that the gambler will end up with $n?
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.