An insurance policy costs $400,and will pay policyholders $10,000 if they suffer a major injury (resulting in hospitalization),or $2,000 if they suffer a minor injury (resulting in lost time from work).The company estimates that each year 1 in every 3,000 policyholders may have a major injury,and 1 in 1,000 a minor injury. Create a probability model for the company's profit on this policy.
A) $$\begin{array} { l | c | c | c }
\text { Profit } & \$ 400 & - \$ 10,400 & - \$ 2,400 \
\hline \text { P(profit) } & 0.9987 & 0.0003 & 0.001
\end{array}$$
B) $$\begin{array} { l | c | c | c }
\text { Profit } & \$ 400 & \$ 10,000 & \$ 2,000 \
\hline \text { P(profit) } & 0.9987 & 0.0003 & 0.001
\end{array}$$
C) $$\begin{array} { l | c | c | c }
\text { Profit } & \$ 400 & \$ 10,400 & \$ 2,400 \
\hline \text { P(profit) } & 0.9987 & 0.0003 & 0.001
\end{array}$$
D) $$\begin{array} { l | c | c | c }
\text { Profit } & \$ 400 & \$ 9,600 & \$ 1,600 \
\hline \text { P(profit) } & 0.9987 & 0.0003 & 0.001
\end{array}$$
E) $$\begin{array} { l | c | c | c }
\text { Profit } & \$ 400 & - \$ 9,600 & - \$ 1,600 \
\hline \text { P(profit) } & 0.9987 & 0.0003 & 0.001
\end{array}$$

Question

An insurance policy costs $400,and will pay policyholders $10,000 if they suffer a major injury (resulting in hospitalization),or $2,000 if they suffer a minor injury (resulting in lost time from work).The company estimates that each year 1 in every 3,000 policyholders may have a major injury,and 1 in 1,000 a minor injury. Create a probability model for the company's profit on this policy.
A) $$\begin{array} { l | c | c | c } 
\text { Profit } & \$ 400 & - \$ 10,400 & - \$ 2,400 \
\hline \text { P(profit) } & 0.9987 & 0.0003 & 0.001
\end{array}$$
B) $$\begin{array} { l | c | c | c } 
\text { Profit } & \$ 400 & \$ 10,000 & \$ 2,000 \
\hline \text { P(profit) } & 0.9987 & 0.0003 & 0.001
\end{array}$$
C) $$\begin{array} { l | c | c | c } 
\text { Profit } & \$ 400 & \$ 10,400 & \$ 2,400 \
\hline \text { P(profit) } & 0.9987 & 0.0003 & 0.001
\end{array}$$
D) $$\begin{array} { l | c | c | c } 
\text { Profit } & \$ 400 & \$ 9,600 & \$ 1,600 \
\hline \text { P(profit) } & 0.9987 & 0.0003 & 0.001
\end{array}$$
E) $$\begin{array} { l | c | c | c } 
\text { Profit } & \$ 400 & - \$ 9,600 & - \$ 1,600 \
\hline \text { P(profit) } & 0.9987 & 0.0003 & 0.001
\end{array}$$

Quizplus · Accepted Answer

The profit is calculated as the premium minus the payout. For no injury, the profit is $400. For a major injury, the profit is $400 - $10,000 = -$9,600. For a minor injury, the profit is $400 - $2,000 = -$1,600. The probabilities are given as 0.9987 for no injury, 0.0003 for a major injury, and 0.001 for a minor injury.

An Insurance Policy Costs $400,and Will Pay Policyholders $10,000 If