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Answer to Question #2826 in Statistics and Probability for alyssa

Question #2826
20% of the deer in a wildlife preservation part are believed to have certain antler infections. A zoologist randomly captures 15 deer and checks their antlers. Assuming the prediction is accurate, determine the probability that more than three of the deer will have infected antlers.
Expert's answer
The number X of deers among n=15 ones having infected antlers has binomial distribution with parameters
p=0.2, q=1-p=0.8,
so
P(X=m) = C(15, m) 0.2m 0.8(15-m)
Hence
P(X>3) = 1-P(X<4) = 1- P(X=0) - P(X=1) - P(X=2) - P(X=3) =
= 1- 0.815 - 15∙0.2∙0.814- (15∙14)/2∙0.22∙0.813 - (15∙14∙13)/(2∙3)∙0.23∙0.812 =
= 1 - 0.03518 - 0.13194 - 0.23090 - 0.25014 = 0.35184

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