Assignment 10

Smith is in jail and has 1 dollar; 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:

  1. he bets 1 dollar each time (timid strategy).
  2. he bets, each time, as much as possible but not more than necessary to bring his fortune up to 8 dollars (bold strategy).
  3. Which strategy gives Smith the better chance of getting out of jail?

A. Timid Strategy

p <- 0.4
q <- 0.6
r <- q/p

QA <- (1-r^1)/(1-r^8)
QA
## [1] 0.02030135

B. Bold Strategy

QB <- dbinom(3,3,p)
QB
## [1] 0.064

C. Better Chance

Smith has a better change using the Bold Strategy however it’s a VERY slim chance this will work.