One-period tree with up move to 110 and down to 80

Interest rates are zero. A stock at $100$ will move in one step either to $110$ (with real-world probability $2/3$) or to $80$. Find the price of a call struck at $100$.

$20/3\approx6.67$. The risk-neutral up probability solves $110q+80(1-q)=100$, so $q=\tfrac23$ (equal here to the real probability, by coincidence). The call pays $10$ up and $0$ down, so it is worth $\tfrac23\times10$. Replication agrees: hold $\tfrac13$ share and borrow $26\tfrac23$.