Question: One of the most important tasks for economists is to make forecasts for the performance (up or down) of investments such as 30-year Treasury bonds. The Journal of Investing (Vol.6, No.2, page 8, 1997) reports that, in a sample of 30 six-month surveys, the consensus estimate of performance for the 30-year Treasury bond has been wrong 20 out of the 30 times!

a. Find the probability that two randomly selected consensus estimates were correct.

b. Find the probability that three randomly selected consensus estimates were wrong.  Edit

Answer: the sample distribution follows binomial distribution with parameter n= 30, p(correct)=10/30= 0.33 and q(incorrect)=20/30=0.67

a.
the probability that two randomly selected consensus estimates were correct=30C2*(0.33)^2*(0.67)^28=0.00639

b. the probability that three randomly selected consensus estimates were wrong=30C3*(0.67)^3*(0.33)^27=0.000000000122  Edit