MATH 110 MODULE 3 EXAM

Module 3 Exam Exam Page 1 Suppose A and B are two events with probabilities: P(Ac )=.40,P(B)=.45,P(A∪B)=.60. Find the following: a) P(A∩B). p(anb) = p(a) + p(b) - p(aub) p(a) = 1 - p(a^c) p(a^c) = 0.40 1 - 0.40 = 0.60 p(a) = 0.60 0.60 + 0.45 - 0.60 = 0.45 P(AnB) = 0.45 b) P(A). p(a) = 1 - p(a^c) p(a^c) = 0.40 1 - 0.40 = 0.60 P(A) = 0.60 c) P(Bc). p(b) = 1 - p(b^c) rearranged to find p(b^c) = 1 - p(b) 1 - 0.45 = 0.55 Exam Page 3 Find the answer to each of the following by first reducing the fractions as much as possible: a) P(850,4)= p(n,r) = n! / (n-r)! n = 850 r = 4 850 - 4 = 846 p(850, 4) = 850! / 846! 850x849x848x847 = 400 P(850,4) = 400 b) C(530,4)= c(n,r) = n! / r! (n-r)! n = 530 r = 4 530 - 4 = 526 c(530,4) = 530! / (4!)(526!) (530x529x528x527) / (4x3x2x1) = 20 / 24= 0 C(530,4) = 0 Answer Key Module 3 Exam Exam Page 1 Suppose A and B are two events with probabilities: P(Ac )=.40,P(B)=.45,P(A∪B)=.60. Find the following: a) P(A∩B). p(anb) = p(a) + p(b) - p(aub) p(a) = 1 - p(a^c) p(a^c) = 0.40 1 - 0.40 = 0.60 p(a) = 0.60 0.60 + 0.45 - 0.60 = 0.45 P(AnB) = 0.45 b) P(A). p(a) = 1 - p(a^c) p(a^c) = 0.40 1 - 0.40 = 0.60 P(A) = 0.60 c) P(Bc). p(b) = 1 - p(b^c) rearranged to find p(b^c) = 1 - p(b) 1 - 0.45 = 0.55 Exam Page 3 Find the answer to each of the following by first reducing the fractions as much as possible: a) P(850,4)= p(n,r) = n! / (n-r)! n = 850 r = 4 850 - 4 = 846 p(850, 4) = 850! / 846! 850x849x848x847 = 400 P(850,4) = 400 b) C(530,4)= c(n,r) = n! / r! (n-r)! n = 530 r = 4 530 - 4 = 526 c(530,4) = 530! / (4!)(526!) (530x529x528x527) / (4x3x2x1) = 20 / 24= 0 C(530,4) = 0 Answer Key