Answer to Question #2826 in Statistics and Probability for alyssa
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.
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