Questions: A venture capitalist, willing to invest 1,000,000, has three investments to choose from. The first investment, a software company, has a 15% chance of returning 4,000,000 profit, a 40% chance of returning 3,500,000 profit, and a 45% chance of losing the million dollars. The second company, a hardware company, has a 13% chance of returning 6,000,000 profit, a 38% chance of returning 500,000 profit, and a 49% chance of losing the million dollars. The third company, a biotech firm, has a 7% chance of returning 11,000,000 profit, a 21% of no profit or loss, and a 72% chance of losing the million dollars. Order the expected values from smallest to largest. third, second, first third, first, second second, first, third first, third, second second, third, first first, second, third

A venture capitalist, willing to invest 1,000,000, has three investments to choose from. The first investment, a software company, has a 15% chance of returning 4,000,000 profit, a 40% chance of returning 3,500,000 profit, and a 45% chance of losing the million dollars. The second company, a hardware company, has a 13% chance of returning 6,000,000 profit, a 38% chance of returning 500,000 profit, and a 49% chance of losing the million dollars. The third company, a biotech firm, has a 7% chance of returning 11,000,000 profit, a 21% of no profit or loss, and a 72% chance of losing the million dollars.

Order the expected values from smallest to largest.  
third, second, first  
third, first, second  
second, first, third  
first, third, second  
second, third, first  
first, second, third
Transcript text: A venture capitalist, willing to invest $\$ 1,000,000$, has three investments to choose from. The first investment, a software company, has a $15 \%$ chance of returning $\$ 4,000,000$ profit, a $40 \%$ chance of returning $\$ 3,500,000$ profit, and a $45 \%$ chance of losing the million dollars. The second company, a hardware company, has a $13 \%$ chance of returning $\$ 6,000,000$ profit, a $38 \%$ chance of returning \$500,000 profit, and a $49 \%$ chance of losing the million dollars. The third company, a biotech firm, has a $7 \%$ chance of returning $\$ 11,000,000$ profit, a $21 \%$ of no profit or loss, and a $72 \%$ chance of losing the million dollars. Order the expected values from smallest to largest. third, second, first third, first, second second, first, third first, third, second second, third, first first, second, third
failed

Solution

failed
failed

Solution Steps

Step 1: Calculate Expected Values

To determine the expected values for each investment, we compute the mean of the profit outcomes weighted by their respective probabilities.

  1. Software Company: \[ \text{Mean} = 4000000 \times 0.15 + 3500000 \times 0.4 + (-1000000) \times 0.45 = 1550000.0 \]

  2. Hardware Company: \[ \text{Mean} = 6000000 \times 0.13 + 500000 \times 0.38 + (-1000000) \times 0.49 = 480000.0 \]

  3. Biotech Firm: \[ \text{Mean} = 11000000 \times 0.07 + 0 \times 0.21 + (-1000000) \times 0.72 = 50000.0 \]

Step 2: Order the Expected Values

Next, we order the expected values from smallest to largest:

  • Biotech Firm: \( 50000.0 \)
  • Hardware Company: \( 480000.0 \)
  • Software Company: \( 1550000.0 \)

Thus, the order of expected values is: \[ \text{third (Biotech), second (Hardware), first (Software)} \]

Final Answer

The order of expected values from smallest to largest is \(\boxed{\text{third, second, first}}\).

Was this solution helpful?
failed
Unhelpful
failed
Helpful