1. J. B. Rhine’s book New Frontiers of the Mind reported results from his ESP experiments. The New York Times science editor was enthusiastic. He noted that some people dismiss Rhine’s results by arguing that, just like in gambling, people can have a run of luck. The writer rejected this suggestion: “The run-of-luck theory has also been invoked with some disregard of the obvious fact that runs of bad luck will cause runs of good luck in the course of 100,000 trials”. Do you agree that a run of bad luck will cause a run of good luck? Explain your reasoning.

2. The random walk model of stock prices states that stock market returns are independent of the returns in other periods; for example, whether the stock market does well or poorly in the coming month does not depend on whether it has done well or poorly during the past month, the past 12 months, or the past120 months. On average, the monthly return on US stocks has been positive about 60 percent of the time and negative about 40 percent of the time. If monthly stock returns are independent with a 0.6 probability of a positive return and a 0.4 probability of a negative return, what is the probability of :

a) 12 consecutive positive returns?

b) 12 consecutive negative returns

c) A positive return, if the return the preceding month was negative