The probabilities for the states of nature are P$($s$1)0\mathrm{.}65,$ P$($s$2)0\mathrm{.}15,$ and P$($s$3)0\mathrm{.}20.$a$.$ What is the optimal decision strategy if perfect information were available?b$.$ What is the expected value for the decision strategy developed in part $($a$)?$c$.$ Using the expected value approach, what is the recommended decision without per$-$fect information? What is its expected value?d$.$ What is the expected value of perfect information