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Decisions Involving Private Information $-$ End of Chapter Problem

$\backslash$table$[[$Individual$,$Probability of using the insurance$],[$Caras$,0\mathrm{.}2],[$Jose$,0\mathrm{.}5],[$Fan$,0\mathrm{.}15],[$Andre$,0\mathrm{.}6],[$Birat$,0\mathrm{.}4]]$

Talia owns a small public relations firm and wants to contract with her insurance provider to offer your employees short$-$term disability insurance. The insurance will pay out $$5,000$ to any worker who misses at least three consecutive weeks of work due to illness or accident that occurs outside of work. Suppose your employees' probabilities of using the insurance in any year are as shown in the accompanying table.

a$.$ Given the probabilities listed in the table of each employee using the insurance, what would be an actuarially fair price to charge each individual?

Caro

Jose: