Consider the following “game”: A marker is placed on the real line at the point zero. On each turn a coin is flip which a 1 printed on one side and a -1 printed on the other.  If the 1 side lands face up, the marker is moved on unit in the positive direction while if the -1 lands heads up then the marker is moved one unit in the negative direction.  If the coin has a probability of \(p\) of landing with the 1 side face up, answer the following questions:

1. Let \(p=\frac12\). After 10000 turns if you had to pick one site to find the marker which would you choose ?
2. Again let \(p=\frac12\). What is the approximate chance that the marker is further then 100 units from this most likely point after 10000 turns ? What is the approximate chance that the marker is further then 300 units from this most likely point after 10000 turns ?
3. Repeat the above questions with \(p=\frac{9}{10}\).