$2.$ How do I do the following problem by hand: A stock is trading at $$50.$ You believe there is a $60\%$ chance the price of the stock will increase by $10\%$ over the next three months. You believe there is a $30\%$ chance the stock will drop by $5\%$ and you think there is only a $10\%$ chance of a major drop in price of $20\%.$ At the money $3$ month puts are available at a cost of $$6\mathrm{.}5.$ What is the expected dollar profit for a writer of a naked put at the end of three months?