Binomial Experiment

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. 

Solution

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The binomial distribution formula is: Pr ( r successes in n trials ) = nCr x pr 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