P$8-5$ Risk and probability Micro$-$Pub lnc$.$ is considering the purchase of one of two microfilm cameras, R and S $.$ Both should provide benefits over a $10-$year period, and each requires an initial investment of $$4,000.$ Management has constructed the accompanying table showing estimates of rates of return and probabilities for pessimistic, most likely, and optimistic results.

a$.$ Determine the range for the rate of return for each of the two cameras.

b$.$ Determine the average return for each camera.

c$.$ The purchase of which camera is riskier? Why?

$\backslash$table$[[,$Camera R$,$Cameras$],[$Ameunt$,$Probability,Amount,Probability$],[$Initial investment,$$4,000,1\mathrm{.}00,$$$4,000,1\mathrm{.}00],[$Annual rate of return$],[$Pessimistic$,20\%,0\mathrm{.}25,15\%,0\mathrm{.}20],[$Most likely,$25\%,0\mathrm{.}50,25\%,0\mathrm{.}55],[$Optimistic$,30\%,0\mathrm{.}25,36\%,0\mathrm{.}25]]$