A trader buys both a call option and a put option for natural gas at the same strike price of $\backslash ($ q$=\backslash$$ $3\backslash )$ per MMBtu. Suppose that the market price $\backslash ($ P $\backslash )$ can be realized at two values $\backslash (\backslash$$ $2\backslash )$ and $\backslash (\backslash$$ $4\backslash )$ with respective probabilities of $\backslash (1/4\backslash )$ and $\backslash (3/4\backslash ).$ a$)$ Find the future value of the call option for the trader. b$)$ Find the future value of the put option for the trader. c$)$ Is a trader buying both of the above options a risk$-$averse or risk$-$seeking trader, why?