$.$ A decision tree is provided.

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$1\mathrm{.}5$

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$3\mathrm{.}5$

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$1\mathrm{.}4$

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$3\mathrm{.}5$

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a$)$ Calculate Expected value $($EV$)$ at every node. Show all the work.

$\mathrm{.}5$ x $5\mathrm{.}0+\mathrm{.}5$ x$-3\mathrm{.}0=1$

$\mathrm{.}5$x$3\mathrm{.}0+\mathrm{.}5$x$0=1\mathrm{.}5$

$\mathrm{.}5$x$1\mathrm{.}8+\mathrm{.}5$x$1\mathrm{.}0=1\mathrm{.}4$

$\mathrm{.}5$ x$8\mathrm{.}0+\mathrm{.}5$ x $-1\mathrm{.}0=3\mathrm{.}5$

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b$)$ What is the optimum decision and EV$?$

c$)$ If your risk tolerance is $$0,$ what is the best decision and EV$?$

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