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∼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−(810)(0.95)8(0.08)10−8−(910)(0.95)9(0.08)10−9−(1010)(0.95)10(0.08)10−10=0.0115
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