What is the probability that at most 3 patients fail to follow up in the first month? 1 comment
Posted at 1:05 pm in Mathematics
A longitudinal study is conducted requiing patients to follow up with research associates every month for assessments. The Probability that a patient fails to follow up in a given month is 10%. A pilot study is conducted to assess feasibility involving 20 patients. What is the probability that at most 3 patients fail to follow up in the first month?
Binomial Distribution Question
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Winnfield III
31 Aug 10 at 1:11 pm
As you noted, this is another problem that involves the application of the binomial theorem. With respect to the particulars of this problem, we have:
1 =
1^20 =
(.1 + .9)^20 =
(C(20,0) ∙ (.1)° ∙ (.9)²°) + (C(20,1) ∙ (.1)¹ ∙ (.9)^19) + (C(20,2) ∙ (.1)² ∙ (.9)^18) + (C(20,3) ∙ (.1)³ ∙ (.9)^17) + … + (C(20,20) ∙ (.1)²° ∙ (.9)°).
where C(a,b) = aCb = (a!)/(b!(a-b)!).
The answer is the sum of the above first three terms:
(C(20,0) ∙ (.1)° ∙ (.9)²°) + (C(20,1) ∙ (.1)¹ ∙ (.9)^19) + (C(20,2) ∙ (.1)² ∙ (.9)^18) + (C(20,3) ∙ (.1)³ ∙ (.9)^17) ≈
(1)∙(1)∙(.12158) + (20)∙(.1)∙(.13509) + (190)(.01)(.15009) + (1,140)(.001)(.16677) ≈
.12158 + .27018 + .28517 + .19012 ≈
.86705