Answer to Question #351052 in Statistics and Probability for Mark

Question

There were ten red bottles sitting on the wall. The probability of a red bottle accidentally falling is 0.95. What is the probability that fewer than 8 of the green bottles accidentally fall?

Answer 1

Since there are no green bottles, then the probability that fewer than 8 of the green bottles accidentally fall is $0.$

Let $X=$ the number of red bottles which fall: $X\sim Bin (n, p).$

Given $n=10, p=0.95, q=1-p=0.05.$

$$P(X<8)=1-P(X=8)-P(X=9)$$ $$-P(X=10)=1-\dbinom{10}{8}(0.95)^{8}(0.08)^{10-8}$$ $$-\dbinom{10}{9}(0.95)^{9}(0.08)^{10-9}-\dbinom{10}{10}(0.95)^{10}(0.08)^{10-10}$$ $$=0.0115$$