Probability - HW 10

Question 1

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

Part A

  1. he bets 1 dollar each time (timid strategy).

Theorem

\[ q_z = \frac{(q/p)^z - 1}{(q/p)^M-1} \] \[ q_z = \frac{(0.6/0.4)^1 - 1}{(0.6/0.4)^8-1} \]

\[ q_1 = 0.0203 \]

Part C

  1. Which strategy gives Smith the better chance of getting out of jail?

The bold strategy gives Smith the better chance of getting out of jail.