Each of three investments has a 20% of becoming worthless within a year of purchase, independently of what happens to the other two investments. If Simone invests an equal sum Q in each of these three investments on January 1, the approximate chance that by the end of the year, she loses no more than 1/3 of her original investment is  Choices.
A) 90% B) 80% C) 70% D) 60% E) 40%
The problem asks for the approximate chance that no more than 1/3 of the original investment is lost. We can apply the “1 – x” technique: what’s the chance that more than 1/3 of the original investment is lost? There are two outcomes we have to separately measure:   (a) All 3 investments become worthless.   (b) 2 of the 3 investments become worthless, while 1 doesn’t.   Outcome (a): The probability is (0.2)(0.2)(0.2) = 0.008, or a little less than 1%.   Outcome (b): Call the investments X, Y, and Z. The probability that X retains value, while Y and Z become worthless, is (0.8)(0.2)(0.2) = 0.032. Now, we have to do the same thing for the specific scenarios in which Y retains value (while X and Z don’t) and in which Z retains value (while X and Y don’t). Each of those scenarios results in the same math: 0.032. Thus, we can simply multiply 0.032 by 3 to get 0.096, or a little less than 10%.   The sum of these two probabilities is   0.008 + 0.096= 
<gadget id="calculator">  0.008 + 0.096</gadget>
<output>0.104</output>
0.104, or a little more than 10%. Finally, subtracting from 100% and rounding, we find that the probability we were looking for is approximately 90%.   The correct answer is A.   This problem illustrates the power of diversification in financial investments. All else being equal, it’s less risky to hold a third of your money in three uncorrelated (independent) but otherwise equivalent investments than to put all your eggs in one of the baskets. That said, be wary of historical correlations! Housing price changes in different US cities were not so correlated—and then they became highly correlated during the recent housing crisis (they all fell together), fatally undermining spreadsheet models that assumed that these price changes were independent.
<result>A</result>
Each of three investments has a 20% of becoming worthless within a year of purchase, independently of what happens to the other two investments. If Simone invests an equal sum Q in each of these three investments on January 1, the approximate chance that by the end of the year, she loses no more than 1/3 of her original investment is