Question #350912
  • 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?
1
Expert's answer
2022-06-16T09:51:28-0400

Since there are no green bottles, then  the probability that fewer than 8 of the green bottles accidentally fall is 0.0.


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

Given n=10,p=0.95,q=1p=0.05.n=10, p=0.95, q=1-p=0.05.



P(X<8)=1P(X=8)P(X=9)P(X<8)=1-P(X=8)-P(X=9)P(X=10)=1(108)(0.95)8(0.08)108-P(X=10)=1-\dbinom{10}{8}(0.95)^{8}(0.08)^{10-8}(109)(0.95)9(0.08)109(1010)(0.95)10(0.08)1010-\dbinom{10}{9}(0.95)^{9}(0.08)^{10-9}-\dbinom{10}{10}(0.95)^{10}(0.08)^{10-10}=0.0115=0.0115




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