Math 120 Binomial experiment

Question

Consider a binomial experiment with n = 8 trials where the probability of success on a single trial is p = 0.15. (For each answer, enter a number. Round your answers to three decimal places.)

(a)

 Find P(r = 0).

 

(b)

 Find P(r ≥ 1) by using the complement rule.

Answer 1

(a)

By the compliment rule,

P(failure)=1-0.15=0.85

P(r=0)=P(8 failures)

By the multiplicative rule for independent events (Binomial events are independent)

P(8 failures)=0.85^8=0.272

Hence P(r=0)=0.272

(b)

By the compliment rule,

P(r>=1)=1-P(r=0)=1-0.272=0.728