an investor has an opportunity to invest in three companies. she researched each company and collected the…

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?\n\n| company | loss, probability of loss | probability to break even | profit, probability of profit |\n| ---- | ---- | ---- | ---- |\n| a | $24,000, 16% | 50% | $10,000, 34% |\n| b | $12,000, 32% | 40% | $21,000, 28% |\n| c | $6,000, 23% | 17% | $5,000, 60% |\n\ncompany a\ncompany b\ncompany c\nall companies have a probability of loss.

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?\n\n| company | loss, probability of loss | probability to break even | profit, probability of profit |\n| ---- | ---- | ---- | ---- |\n| a | $24,000, 16% | 50% | $10,000, 34% |\n| b | $12,000, 32% | 40% | $21,000, 28% |\n| c | $6,000, 23% | 17% | $5,000, 60% |\n\ncompany a\ncompany b\ncompany c\nall companies have a probability of loss.

Answer

Explanation:

Step1: Calculate expected value for company A

The expected - value formula is $E(X)=\sum_{i}x_ip_i$. For company A, the expected value $E_A$ is: [ \begin{align*} E_A&=(- 24000)\times0.16 + 0\times0.5+10000\times0.34\ &=-3840 + 0+3400\ &=-440 \end{align*} ]

Step2: Calculate expected value for company B

For company B, the expected value $E_B$ is: [ \begin{align*} E_B&=(-12000)\times0.32 + 0\times0.4+21000\times0.28\ &=-3840+0 + 5880\ &=2040 \end{align*} ]

Step3: Calculate expected value for company C

For company C, the expected value $E_C$ is: [ \begin{align*} E_C&=(-6000)\times0.23+0\times0.17 + 5000\times0.6\ &=-1380+0+3000\ &=1620 \end{align*} ]

Step4: Compare expected values

Since $E_B = 2040$, $E_C=1620$ and $E_A=-440$, and $2040>1620>-440$.

Answer:

B. company B