$($Pricing a call option by no arbitrage.$)$ There are $2$ states. The price asset $1,$

a risk$-$free asset is $1.$ The price of asset $2,$ a stock, is $3.$ We want to find the price of a call

option on the stock with strike price $4.$ The call option gives you the right $($but not the

obligation$)$ to buy the stock at price $4$ after you learn which state you are in$.$

states $12$ price

asset $1($risk$-$free$)11$

$1$

asset $2($stock$)26$

$3$

asset $3($call option$)??$

$?$

$12$

$($a$)$ Write the payoffs of the call option $$ call it asset $3.$

$($b$)$ Find the price of the call option.