Under normal economic conditions, with a 45% probability of occurring, King can expect to earn a net income of $50,000 per year. In a mini-recession, at 25% probability, King will earn $20,000. In a severe recession, at a 20% probability, King will lose $10,000. There is also a slight probability (10%) that King will lose $300,000 if the expansion fails and the branch office must be closed. Should King open a branch office in California?

answer the probability is in Kings favor and the most he would lose is $10,000 and that is in a severe recession. Correct

Are you asking if this is correct? (If so, put a ? Mark after it so we know.) Or are you saying this is supposed to be the correct answer and you don't understand why?

I saw where you posted this elsewhere -- either homework help or math or something, and what you were told there about the (4500) is what I'd consider the correct answer. I don't recall where you posted that, but you should take a look at that one.