Stock price is $15$ today. In a year, it has $50-50$ chances of going up or down. If it goes up, then $0.8$ probability of the price being $25$. If it goes down, then $0.4$ probability of price being $5$ and $0.6$ probability of it being $0$. Find the price of $call$ $option$ at strike $25$.
My approach:
I think I should, first of all, find the value of the stock on the up branch of the tree that happens with a probability of 0.2. I don't know though how to find such value.
I thought to include in the reasoning the formulas of $p,u,d$ of the tree, but it doesn't seem to help.
This is the tree I am talking about. Nevertheless, in this problem, the tree should have only one node so $n=1$, and since the maturity is 1 year, t should also be 1, $t=1$