# Question

One theory concerning the S& P 500 Index is that if it in-creases during the first five trading days of the year, it is likely to increase during the entire year. From 1950 through 2013, the S& P 500 Index had these early gains in 41 years (in 2011 there was virtually no change). In 36 of these 41 years, the S& P 500 Index increased for the entire year. Assuming that this indicator is a random event with no predictive value, you would expect that the indicator would be correct 50% of the time. What is the probability of the S& P 500 Index increasing in 36 or more years if the true probability of an increase in the S& P 500 Index is

a. 0.50?

b. 0.70?

c. 0.90?

d. Based on the results of (a) through (c), what do you think is the probability that the S& P 500 Index will increase if there is an early gain in the first five trading days of the year? Explain.

a. 0.50?

b. 0.70?

c. 0.90?

d. Based on the results of (a) through (c), what do you think is the probability that the S& P 500 Index will increase if there is an early gain in the first five trading days of the year? Explain.

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