##### Question

In: Statistics and Probability

# your aunt comes to you with an investment opportunity. She needs you to invest $500,000. If... your aunt comes to you with an investment opportunity. She needs you to invest$500,000. If the investment succeed, it will pay you back your investment plus an additional $2 million. If it fails you get nothing back. She thinks there is a 30% chance of success. a. what is the expected value of the investment? b. what is the most likely outcome? ## Solutions ##### Expert Solution a.  Returns(X) Probability(P) XP Success 7,000,000 0.30 2,100,000 Failure 0 0.70 0 Expected value ==> 2,100,000 b. Most likely outcome: Expected value =$ 1,867,600 ( As per following calculation)

 Returns(X) Probability(P) XP Success 7,000,000 0.2668 1,867,600 Failure 0 0.7332 0 Expected value ==> 1,867,600

To find most likely outcome:

The following simulation of 9 trials using Binomial distribution was conducted and we find most likely

probability of success = 0.2668.

 Trials Probability of success 1 0.1211 2 0.2335 3 0.2668 4 0.2001 5 0.1029 6 0.0368 7 0.0090 8 0.0014 9 0.0001

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