Binomial Experiment

Question

Consider a binomial experiment with n = 9 trials

 where the probability of success on a single trial is p = 0.15.

 (Round your answers to three decimal places.)

(a) Find P(r = 0).

 

 

(b) Find P(r ≥ 1)

 by using the complement rule. 

Answer 1

The binomial distribution formula is: Pr ( r successes in n trials ) = nCr x p^r x ( 1 - p )^(n-r) where nCr is the number of combinations of nobjects gtaken r at a time, p is probability of success & (1-p) the probability of failure. We have for a)

Pr ( r = 0 ) = 9C0 x .15⁰ x .85⁹ = 1 x 1 x .232 = .232 For b)

Pr ( r ≥ 1 ) = 1 - Pr ( r = 0 ) = 1 - .232 = .768