Smith is in jail and has 3 dollars; he can get out on bail if he has 8 dollars.

Smith is in jail and has 3 dollars; he can get out on bail
if he has 8 dollars. A guard agrees to make a series of bets with him. If Smith
bets A dollars he wins A dollars with probability .4 and loses A dollars with
probability .6.Find the probability that he wins 8 dollars before losing
all of his money if(a) he bets 1 dollar each time (timid strategy).(b) he bets each time as much as possible but not more
than necessary to bring his fortune up to 8 dollars (bold strategy).(c) Which strategy gives Smith the better chance of getting
out of jail?