binomial distribution

Question

Find the probability of having 2,3, or 4 successes in five trials of a binomial experiment in which the probability of success is 40% Round to the nearest tenth of a percent.

Answer 1

(5C2)(.4^2)(.6^3) + (5C3)(.4^3)(.6^2) + (5C4)(.4^4)(.6^1)

= 10(.16)(.216) + 10(.064)(.36) + 5(.0256)(.6) = .6528

Multiply by 100 to get % and then round, giving 65.3%

Note the notation for combinations, such as 5C2 can be calculated as 5!/(2!3!) = 5 X 4 / (2 X 1) = 10.

The factorial 3! cancels the denominator with all multiplications in the numerator involving 3 and below, leaving only 5 and 4.