A simplified model for the movement of the price of stock supposes that on each day the stock's prices either moves up 1 unit with probability p or moves down 1 unit with probability 1-p. The changes on different days are assumed to be independent.
a. What is the probability that after 2 days the stock will be at its original price?
b. What is the probability that after 3 days the stock's price will have increased by 1 unit?
c. Given that after 3 days the stock's price has increased by 1 unit, what is the probability that it went up on the first day?