Backing Out the Approval Odds

A single-drug biotech trades at $\$42$ per share. A regulator announces its decision tomorrow morning. Analysts agree that on approval the company is worth $\$70$ per share and on rejection it is worth $\$18$ per share, with no other outcome possible. Ignore the one day of interest.

(a) What probability of approval is the market pricing?

(b) Your own research says the true probability is $55\%$. What is the trade, and how big is the edge?

(c) Name two reasons the number in (a) might not equal the market's genuine belief.