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An investor has an opportunity to invest in three companies. She researched each company and collected the information in the table below. Which company would provide the best investment?

\begin{tabular}{|c|c|c|c|}
\hline \multicolumn{4}{|c|}{ Probability of Profit and Loss by Company } \\
\hline Company & \begin{tabular}{c}
Loss, \\
Probability of Loss
\end{tabular} & \begin{tabular}{c}
Probability to Break \\
Even
\end{tabular} & \begin{tabular}{c}
Profit, \\
Probability of Profit
\end{tabular} \\
\hline A & [tex]$\$[/tex] 24,000, 16\%[tex]$ & $[/tex]50\%[tex]$ & $[/tex]\[tex]$ 10,000, 34\%$[/tex] \\
\hline B & [tex]$\$[/tex] 12,000, 32\%[tex]$ & $[/tex]40\%[tex]$ & $[/tex]\[tex]$ 21,000, 28\%$[/tex] \\
\hline C & [tex]$\$[/tex] 6,000, 23\%[tex]$ & $[/tex]17\%[tex]$ & $[/tex]\[tex]$ 5,000, 60\%$[/tex] \\
\hline \hline
\end{tabular}

A. Company A
B. Company B
C. Company C

(Note: All companies have a probability of loss.)



Answer :

GinnyAnswer
To determine which company would provide the best investment opportunity, we need to calculate the expected value for each company. The expected value is a measure that combines potential outcomes (profit or loss) with the probabilities of those outcomes. It gives us a single numerical value to compare different investment choices.

Here's the step-by-step process to calculate the expected value for each company:

1. Company A:
- Loss amount: [tex]$24,000 - Probability of loss: 0.16 - Profit amount: $[/tex]10,000
- Probability of profit: 0.34
- Probability to break even: 0.50 (which means neither profit nor loss)

The expected value (EV) is calculated as:
[tex]\[ EV_A = (\text{Loss amount} \times \text{Probability of loss}) + (\text{Break even amount} \times \text{Probability to break even}) + (\text{Profit amount} \times \text{Probability of profit}) \][/tex]
Since the break even amount is [tex]$0$[/tex]:
[tex]\[ EV_A = (24000 \times 0.16) + (0 \times 0.50) + (10000 \times 0.34) \][/tex]

2. Company B:
- Loss amount: [tex]$12,000 - Probability of loss: 0.32 - Profit amount: $[/tex]21,000
- Probability of profit: 0.28
- Probability to break even: 0.40

Using the same formula:
[tex]\[ EV_B = (12000 \times 0.32) + (0 \times 0.40) + (21000 \times 0.28) \][/tex]

3. Company C:
- Loss amount: [tex]$6,000 - Probability of loss: 0.23 - Profit amount: $[/tex]5,000
- Probability of profit: 0.60
- Probability to break even: 0.17

Again, using the same formula:
[tex]\[ EV_C = (6000 \times 0.23) + (0 \times 0.17) + (5000 \times 0.60) \][/tex]

Now, the expected values for each company are:
- EV_A = 7240.0
- EV_B = 9720.0
- EV_C = 4380.0

Finally, we compare the expected values:
The best investment is the company with the highest expected value.

From the calculated values, Company B has the highest expected value of 9720.0.

Therefore, Company B provides the best investment opportunity based on the given probabilities and amounts of profit and loss.

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