The current price of American Airlines stock is $$6.$ In the next year, this stock price can either go up by $$3\mathrm{.}50$ or go down by $$2.$ The stock pays no dividends. The one$-$year risk$-$free interest rate is $3\%$ and will remain constant.

a$)$

Calculate the risk$-$neutral probabilities.

b$)$

Use the risk$-$neutral probabilities you found in part a$)$ to calculate the price of a one$-$year call option on American Airlines stock with a strike price of $$7.$