A day trader buys an option on a stock that will return $150 profit if the stock goes up today and loses $250 if it goes down. If the trader thinks there is a 80% chance that the stock will go up, what is his expected profit on the option today?

I am lost as to how to do this problem can anyone help?

The expected return is calculated by multiplying the probability for each outcome by the amount that would be received, and adding up the results. For this problem there is an 80% chancwof making $150, and hence a 20% chance of losing $250, so the expected return is:

0.80 x $150 + 0.20 x (-$250) = $120 - $50 = $70

What this means is that if the trader could play this game many times over on average he should make $70 each time he plays. For example if he played this game 10 times he could expect to win 8 times and lose twice, so he would end up with 8 x $150 - 2 x $250 = $700. That's $70 per game.