a venture capitalist, willing to invest $1,000,000, has three investments to choose from. the first…

a venture capitalist, willing to invest $1,000,000, has three investments to choose from. the first investment, a software company, has a 7% chance of returning $11,000,000 profit, a 21% chance of returning $1,000,000 profit, and a 72% chance of losing the million dollars. the second company, a hardware company, has a 12% chance of returning $7,000,000 profit, a 21% chance of returning $2,000,000 profit, and a 67% chance of losing the million dollars. the third company, a biotech firm, has a 10% chance of returning $4,000,000 profit, a 22% of no profit or loss, and a 68% chance of losing the million dollars. order the expected values from smallest to largest. third, second, first second, first, third first, second, third first, third, second third, first, second second, third, first
Answer
Explanation:
Step1: Calculate expected - value for first company
The formula for expected value $E(X)=\sum_{i}x_ip_i$. For the first company: $E_1 = 0.07\times11000000+0.21\times1000000 + 0.72\times(- 1000000)$ $E_1=770000 + 210000-720000$ $E_1 = 260000$
Step2: Calculate expected - value for second company
$E_2=0.12\times7000000 + 0.21\times2000000+0.67\times(-1000000)$ $E_2 = 840000+420000 - 670000$ $E_2=590000$
Step3: Calculate expected - value for third company
$E_3=0.1\times4000000+0.22\times0+0.68\times(-1000000)$ $E_3 = 400000+0 - 680000$ $E_3=-280000$
Step4: Order the expected values
Since $E_3=-280000$, $E_1 = 260000$, $E_2=590000$, the order from smallest to largest is third, first, second.
Answer:
third, first, second