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# Binomial Probability: S&P 500 Stock Index

Compared with almost any other investment alternative, the stock market performed especially well during the 1990s. In fact, there were only two years out of ten years during the 1990s when the S&P 500 stock index failed to give an annual return on investment of 12 percent or more. So, based on this ten year period, the probability of receiving less than a 12 percent return per year on the S&P 500 stock index in any given year was only 0.20. If it is assumed that this trend will continue during the 2000s and that the Binomial Distribution applies:

a. Define in words the Binomial Random Variable X applicable to parts b, c and d, i.e., X = ???

b. In the next 8 years, what is the probability of exactly four years of less than 12 percent returns.

c. In the next 8 years, what is the probability of from one to five years of less than 12 percent returns.

d. In the next 8 years, what is the probability of more than three years of less than 12 percent returns.

#### Solution Summary

The solution provides step by step method for the calculation of binomial probabilities. Formula for the calculation and Interpretations of the results are also included.

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