Stocks. Since the stock market began in 1872, stock prices have risenabout 73% o
ID: 2954790 • Letter: S
Question
Stocks.Since the stock market began in 1872, stock prices have risenabout 73% of the years. Assuming that market performance isindependent from year to year, what's the probability that a) the market will rise for 3 consecutive years? b) the market will rise for 3 years out of the next 5? c) the market will fall during at least 1 of the next 5years? d) the market will rise during a majority of years over thenext decade?
Since the stock market began in 1872, stock prices have risenabout 73% of the years. Assuming that market performance isindependent from year to year, what's the probability that a) the market will rise for 3 consecutive years? b) the market will rise for 3 years out of the next 5? c) the market will fall during at least 1 of the next 5years? d) the market will rise during a majority of years over thenext decade?
Explanation / Answer
Treat it as a Binomial variable a) P(rise next three years) = .733=.389 b) P(rise 3 of next 5) =(5C3)(.733)(1-.73)2=10(.389)(.073)= 0.284 c) P(Fall at least once) = 1 - P(Rises all five) = 1 -.735 = 0.793 d) P(majority) = P(6 of 10)+P(7 of 10) + P(8 of 10) + P(9 of 10) +P(10 of 10) = 0.896