The amount of risk in each plan is a measure of the expected value of the plans.
Plan A has the least amount of risk
For plan A, we have:
[tex]\left[\begin{array}{cc}Payout&P(Payout)\\-\$5000&0.14&\$30000&0.37&\$55000&0.49\end{array}\right][/tex]
The expected value of the plan is:
[tex]Plan = \sum Payout \times P(Payout)[/tex]
So, we have:
[tex]Plan\ A= -\$5000 \times 0.14 + \$30000 \times 0.37 + \$55000 \times 0.49[/tex]
[tex]Plan\ A= \$37350[/tex]
For plan B, we have:
[tex]\left[\begin{array}{cc}Payout&P(Payout)\\\$5000&0.34&\$30000&0.26&\$60000&0.4\end{array}\right][/tex]
The expected value of the plan is:
[tex]Plan = \sum Payout \times P(Payout)[/tex]
So, we have:
[tex]Plan\ B = \$5000 \times 0.34 + \$30000 \times 0.26 + \$60000 \times 0.4[/tex]
[tex]Plan\ B = \$33500[/tex]
The expected value of plan A is greater than the expected value of plan B.
This means that: Plan A has the least amount of risk
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