A gambler bets on coin flips. With each flip, he wins $1$ dollar with probability $p$, and loses $1$ dollar with probability $1-p$. He starts with $2$ dollar and stops when he reaches either $0$ or $5$ dollar.
What is the probability that the gambler has $\$5$ in the end?
What is the expected number of coin flips he bets on?
Ok, so basically my assumption towards these question is that:
- Since $p$ and $1-p$ have been specified, its a biased coin.
- The steps are $0$ to $5$, and it starts from step $2$.
Could anyone please confirm or maybe write down your answers if this is correct? or if I have left out any answers could any experts please help me with this question? Your help is much appreciated.