Consider a stock XYZ, whose price either goes up or down by exactly $1 each day. Suppose that XYZ's price goes up $1 with probability p and that...

Consider a stock XYZ, whose price either goes up or down by exactly $1 each day. Suppose that XYZ’s price goes up $1 with probability p and that XYZ’s daily price changes are independent across days. What is value p that makes the probability that the stock price is changed equal 0.5 after two days?

What formula should be used here and why?  Should we use Prob (Count | n,p) = [n!/count!(n-count!]*p^count (1-p)^n-count.  The solution suggests using p(1-p) only.