Payoff Table: Choices: D$1,$ D$2,$ D$3.$ States of Nature: S$1,$ S$2,$ S$3.$ Profit$($ in millions$)$ for each of the States of Nature are given below: For D$1$: $$100,$ $$400,$ $$500.$ For D$2$:$-$$$100,$ $$500,$ $$900.$ For D$3$: $-$$$200,$ $$500,$ $$1600.$ P$($s$1)=0\mathrm{.}4,$ P$($s$2)=0\mathrm{.}4,$ P$($s$3)=0\mathrm{.}2.$ Sample Information Data: Market Research Firm provides following data: conditional probabilities: P$($Fav$/$s$1)=0\mathrm{.}40,$ P$($Fav$/$s$2)=0\mathrm{.}5,$ P$($Fav$/$s$3)=0\mathrm{.}9.$ Then P$($s$1/$Fav$)=$

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$0\mathrm{.}296$

$0\mathrm{.}874$

$0\mathrm{.}756$