b$.$ A company is considering two mutually exclusive projects $S$ and $T.$ Project $S$ Costs Tk$.$

$10$

$30,000$ and project T Tk$.36,000.$ The following particulars relate to these projects:

$\backslash$table$[[$Year$,$Project S$,$Project T$],[$NPV$($TK$.),$Probability,NPV$($TK$.),$Probability$],[1,3000,0\mathrm{.}1,-3000,0\mathrm{.}2],[2,6000,0\mathrm{.}4,6000,0\mathrm{.}3],[3,12000,0\mathrm{.}4,12000,0\mathrm{.}3],[4,15000,0\mathrm{.}1,15000,0\mathrm{.}2]]$

Required: i$)$ Compute the expected cash flows of the projects. ii$)$ Compute the risk attached to each project. iii$)$ Compute the profitability index of each project. iv$)$ Which project do you consider riskier and why? Comment on the result.

Please give a proper mathematical solution step by step without using excel