Hugh buys $8000 worth of stock in an electronics company which he hopes to sell afterward at a profit.The company is developing a new laptop computer and a new desktop computer.If it releases both computers before its competitor,the value of Hugh's stock will jump to $21,000.If it releases one of the computers before its competitor,the value of Hugh's stock will jump to $17,000.If it fails to release either computer before its competitor,Hugh's stock will be worth only $5000.Hugh believes that there is a 40% chance that the company will release the laptop before its competitor and a 50% chance that the company will release the desktop before its competitor. Create a probability model for Hugh's profit.Assume that the development of the laptop and the development of the desktop are independent events.
A) $$\begin{array} { l | c c c }
\text { Profit } & \$ 21,000 & \$ 17,000 & \$ 5000 \
\hline \text { P(Profit } ) & 0.2 & 0.5 & 0.3
\end{array}$$
B) $$\begin{array} { | l | c c c | }
\hline \text { Profit } & \$ 13,000 & \$ 9000 & - \$ 3000 \
\hline \text { P(Profit } ) & 0.2 & 0.5 & 0.3
\end{array}$$
C) $$\begin{array} { | l | c c c | }
\hline \text { Profit } & \$ 13,000 & \$ 9000 & - \$ 3000 \
\hline \text { P(Profit } ) & 0.2 & 0.2 & 0.3
\end{array}$$
D) $$\begin{array} { l | c c c }
\text { Profit } & \$ 21,000 & \$ 17,000 & \$ 5000 \
\hline \text { P(Profit) } & 0.2 & 0.9 & 0.3
\end{array}$$
E) $$\begin{array} { l | c c c }
\text { Profit } & \$ 13,000 & \$ 9000 & - \$ 3000 \
\hline \text { P(Profit } ) & 0.9 & 0.2 & 0.3
\end{array}$$

Question

Hugh buys $8000 worth of stock in an electronics company which he hopes to sell afterward at a profit.The company is developing a new laptop computer and a new desktop computer.If it releases both computers before its competitor,the value of Hugh's stock will jump to $21,000.If it releases one of the computers before its competitor,the value of Hugh's stock will jump to $17,000.If it fails to release either computer before its competitor,Hugh's stock will be worth only $5000.Hugh believes that there is a 40% chance that the company will release the laptop before its competitor and a 50% chance that the company will release the desktop before its competitor. Create a probability model for Hugh's profit.Assume that the development of the laptop and the development of the desktop are independent events.
A) $$\begin{array} { l | c c c } 
\text { Profit } & \$ 21,000 & \$ 17,000 & \$ 5000 \
\hline \text { P(Profit } ) & 0.2 & 0.5 & 0.3
\end{array}$$
B) $$\begin{array} { | l | c c c | } 
\hline \text { Profit } & \$ 13,000 & \$ 9000 & - \$ 3000 \
\hline \text { P(Profit } ) & 0.2 & 0.5 & 0.3
\end{array}$$
C) $$\begin{array} { | l | c c c | } 
\hline \text { Profit } & \$ 13,000 & \$ 9000 & - \$ 3000 \
\hline \text { P(Profit } ) & 0.2 & 0.2 & 0.3
\end{array}$$
D) $$\begin{array} { l | c c c } 
\text { Profit } & \$ 21,000 & \$ 17,000 & \$ 5000 \
\hline \text { P(Profit) } & 0.2 & 0.9 & 0.3
\end{array}$$
E) $$\begin{array} {            l | c c c } 
\text { Profit } & \$ 13,000 & \$ 9000 & - \$ 3000 \
\hline \text { P(Profit } ) & 0.9 & 0.2 & 0.3
\end{array}$$

Quizplus · Accepted Answer

The profits are calculated by subtracting the initial investment ($8000) from the potential values of the stock ($21,000, $17,000, and $5,000), resulting in profits of $13,000, $9,000, and -$3,000, respectively. The probability of both products being released first (and thus earning the highest profit) is the product of their independent probabilities (0.4 for the laptop and 0.5 for the desktop), which is 0.4 * 0.5 = 0.2. The probability of neither being released first is the product of their failure probabilities, 0.6 * 0.5 = 0.3. The remaining probability (1 - 0.2 - 0.3 = 0.5) corresponds to the scenario where only one product is released first.