The Arrow$-$Debreu model has three states and three assets: one is risk$-$free and two are risky. The initial price vector is

$.$ The payoff matrix is:

$($a$)$ Find the state price vector:

$($b$)$ Find the rate of return on the risk$-$free asset $($as percentage$)$:

$\%$

$($c$)$ Find the no$-$arbitrage price of Arrow$-$Debreu security

$.$