Of patients going to a primary care physicianSolutionLet A

Of patients going to a primary care physician

Let A = referrd to a specialist

B = require lab work

Given

P(A) = 0.3

P(B) = 0.4

P((A u B)^c) = 0.35

So P(A u B) = 1 - 0.35 = 0.65

a.) P( both lab work and referral to specialist) = P(A n B) = P(A) + P(B) - P(A u B) = 0.3 + 0.4 - 0.65 =0.05

b.) Now n = 5 , p = 0.3

P(all 5) = (0.3)^5 = 0.00243

c.) n = 5, p = 0.3

P(atleat one) = 1 - P(none) = 1 - (0.7)^5 = 1 - 0.16807 = 0.83193