I'm working on a homework problem involving conditional probability.
A simplified 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
por moves down 1 unit with probability
1 − p. The changes on different days are assumed to be independent.
What is the probability that after 3 days the stock’s price will have increased by 1 unit?
I believe there are 8 possible outcomes for 3 days, and that 3 of these outcomes would result in the desired change of +1. I think the probability would be 3/8 if both outcomes were equally likely but it doesn't seem that they are.
How do I go about factoring in the p and p-1 information? Is this a binomial problem where the resulting answer would be something like (8 choose 3)(p^3)(p-1)^8? Any hints or helpful resources would be appreciated.