MANAGERIAL STATISTICS - Please provide work and detailed answer! Thanks in advance:

1. QUESTION: The random walk model. It is widely recognized that the direction the stock market moves often appears to be completely random and independent from day to day. This is usually described as the random walk model, and this model is used by most options traders on Wall Street and is studied by Nobel prize economists. The simplest random walk model assumes that during any given day a stock's price has a 50% chance of going up and a 50% chance of going down, regardless of what happened in the past. Under this random walk model,

what is the chance a stock's price goes up the next two days in a row?

what is the chance it goes in the same direction for two days in a row, and then changes direction on the third day?