An investor is considering a $10,000 investment in a start-up company. She es; mates that she has probability 0.25 of a $20,000 loss, probability 0.20 of a $10,000 profit, probability 0.15 of a $50,000 profit, and probability 0.40 of breaking even (a profit of $0). What is the expected value of the profit? Would you advise the investor to make the investment?

The expected value of profit is 4,500$ and I would advise the investor to make the investment.

Step-by-step explanation:

Used Terminologies:

In general, the expected profit is calculated by using following equation:

E (Profit_x) = (Probability of x) * (Profit in x scenario)

E (Profit) = Total Expected Profit = Sum of expected profits from all possible outcomes

E (Profit_A) = Expected Profit against possible outcome A.

E (Profit_B) = Expected Profit against possible outcome B.

E (Profit_C) = Expected Profit against possible outcome C.

E (Profit_D) = Expected Profit against possible outcome D.

We have 4 possible outcomes with 4 different possibilities as under:

Possible Outcome 1 (A) : She has 0.25 probability of 20,000$ profit

E (Profit_A) = (Probability of A) * (Profit from scenario A)

E (Profit_A) = 0.25 * (-20,000)

E (Profit_A) = - 5,000$

Similarly we have from Possible Outcomes 2 (B), 3 (C) & 4 (D) as under respectively:

E (Profit_B) = 0.2 * (10,000)

E (Profit_B) = 2,000$

E (Profit_C) = 0.15 * 50,000

E (Profit_C) = 7,500$

E (Profit_D) = 0.4 * 0

E (Profit_D) = 0$

Therefore we have total expected profit from the investment as:

E (Profit) = E (Profit_A) + E (Profit_B) + E (Profit_C) + E (Profit_D)

E (Profit) = - 5000 + 2000 + 7500 + 0

E (Profit) = 4,500$