Question

1. A gambler begins with $500, each game, he may win $100 with a probability 0.7 or lose $ 100 with probability 0.3. He will play until he either doubles his money or loses it all. Use simulation to determine how long he can expect to play the game, and estimate the probability that he doubles his money.

Answer 1

In this event gambler plays up to either he doubles his amount or loose all his amount.

Given in question that

Initially money in hand is 500 $

Probability of winning the Gamble's is 0.7

Probability of loosing the Gamble's is 0.3

He the gambler keeps on winning his amount let the number of steps to double his amount be a and if keeps on loosing let the minimum number of steps to make it zero is b.

​​​​​​From the Simulation diagram

a=5, b=5.

Now probability that he doubles his amount is calculated in solution 2.