Problem 2 A simplifed model for the movement of the price of a stock supposes that on each day the stock's price 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. 1. What is the probability that after 2 days the stock will be at its original price? 2. What is the probability that after 3 days the stock's price will have increased by 1 unit? 3. 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?

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