Final answer:
To calculate the probability of losses in the project, we need to analyze the probability distribution functions for each investment and determine the chance of losing the investment. By multiplying the individual probabilities, we can find the overall probability of the project resulting in losses, which is 4.8%.
Step-by-step explanation:
To find the probability of losses (negative rates of return), we need to consider each investment's probability distribution function (PDF) and calculate the probability of losing the investment. Let's start with the first investment: The first investment has a 60% chance of losing $1,000,000. Since we are only interested in losses, the probability of losing this investment is 60%.Now let's move on to the second investment. The second investment has a 40% chance of losing $1,000,000. So, the probability of losing this investment is 40%.
Finally, for the third investment, there is a 20% chance of losing $1,000,000. Therefore, the probability of losing this investment is 20%.
To calculate the overall probability of losing any of the investments, we need to find the joint probability of all three investments resulting in losses. Since these events are independent, we can multiply the individual probabilities together. Thus, the overall probability of the project resulting in losses is:
Total probability of losses = 0.6 x 0.4 x 0.2 = 0.048 or 4.8%.