Probability and Statistics

Question

Find the probability of at least one failure in five trials of a binomial experiment in which the probability of success is 30%. Round to the nearest tenth of a percent.

Answer 1

X ~ Bin(n = 5,p = 3/10)

 

P(X < 5) = 1 - P(X = 5)

 

= 1 - C(5,5)(3/10)⁵(1 - 3/10)⁰

 

= 1 - 3⁵/10⁵

 

= (10⁵ - 3⁵)/10⁵

 

= 99757/100000

 

= 99.757%

 

This rounds to 99.8%.