Statistics

Question

Find the probability of exactly two success in five trials of a binomial experiment in which the probability of success is 50%. Round to the nearest tenth of a percent.

Answer 1

(p+q)⁵ is the binomial distribution with 5 trials. in your case, p = 0.5 so q also = 0.5

Note that this is 1⁵ = 1, and that the binomial expansion gives 6 terms, each being a probability of # of successes, from 0 to 5.

 

The term that you want is ₅C₂•p²•q³ representing 2 successes and 3 failures.  This term's value is

(5C2)(0.5⁵) = 10•0.03125 = 0.3125 = P(2 successes in 5 trials) =31.3% rounded to nearest tenth of a percent.