binomial distributions

Question

Find the probability of at least three successes in six trials of a binomial experiment in which the probability of success is 50%. Round to the nearest tenth of a percent. I CANT CALCULATE THE RIGHT ANSWER

Answer 1

Use the standard formula to calculate probability of 3 successes, 4 successes, 5, and 6, and then add them together.

(6C3)(.5³.5³) + (6C4)(.5⁴.5²) + (6C5)(.5⁵.5¹) + (6C6)(.5⁶.5⁰)

= (6C3 + 6C4 + 6C5 + 6C6)(.5⁶)

= [6 X 5 X 4/(3 X 2) + 6 X 5/(2) + 6/1 + 1](.5⁶)

= (20 + 15 + 6 + 1)/64

= 42/64

= 0.65625

= 65.6% to the nearest tenth of a percent.