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

A. Company [tex]$A$[/tex]
B. Company [tex]$B$[/tex]
C. Company [tex]$C$[/tex]

To evaluate which company would provide the best investment for the investor, we need to calculate the expected value (EV) for each company. The expected value helps us understand the average outcome of an investment when considering all possible profits and losses along with their probabilities.

The formula to calculate the expected value is:
[tex]\[ \text{Expected Value (EV)} = (\text{Loss Amount} \times \text{Probability of Loss}) + (\text{Profit Amount} \times \text{Probability of Profit}) + (0 \times \text{Probability to Break Even}) \][/tex]

Let's calculate the expected values for each company step-by-step.

### Company A:
- Loss: $ -$24,000 $
- Probability of Loss: $ 16\% = 0.16 $
- Probability to Break Even: $ 50\% = 0.50 $
- Profit: $ $10,000 $
- Probability of Profit: $ 34\% = 0.34 $

Expected Value for Company A:
[tex]\[ \text{EV}_A = (-24000 \times 0.16) + (0 \times 0.50) + (10000 \times 0.34) \][/tex]
[tex]\[ \text{EV}_A = -3840 + 0 + 3400 \][/tex]
[tex]\[ \text{EV}_A = -440 \][/tex]

### Company B:
- Loss: $ -$12,000 $
- Probability of Loss: $ 32\% = 0.32 $
- Probability to Break Even: $ 40\% = 0.40 $
- Profit: $ $21,000 $
- Probability of Profit: $ 28\% = 0.28 $

Expected Value for Company B:
[tex]\[ \text{EV}_B = (-12000 \times 0.32) + (0 \times 0.40) + (21000 \times 0.28) \][/tex]
[tex]\[ \text{EV}_B = -3840 + 0 + 5880 \][/tex]
[tex]\[ \text{EV}_B = 2040 \][/tex]

### Company C:
- Loss: $ -$6,000 $
- Probability of Loss: $ 23\% = 0.23 $
- Probability to Break Even: $ 17\% = 0.17 $
- Profit: $ $5,000 $
- Probability of Profit: $ 60\% = 0.60 $

Expected Value for Company C:
[tex]\[ \text{EV}_C = (-6000 \times 0.23) + (0 \times 0.17) + (5000 \times 0.60) \][/tex]
[tex]\[ \text{EV}_C = -1380 + 0 + 3000 \][/tex]
[tex]\[ \text{EV}_C = 1620 \][/tex]

### Comparison of the Expected Values:
- Expected Value of Company A: $ -440 $
- Expected Value of Company B: $ 2040 $
- Expected Value of Company C: $ 1620 $

Based on the expected values calculated, Company B has the highest expected value of $ 2040 $, followed by Company C with $ 1620 $, and Company A with $ -440 $.

Therefore, the best investment for the investor would be Company B.