Question

Suppose that a company produces three different versions of an operating sys- tem: basic, extended and complete. Out of the people who purchased the basic version, 10% consider themselves advanced users. Out of the people who pur- chased the extended version, 40% consider themselves advanced users. Out of the people who purchased the complete version, 80% consider themselves ad- vanced users. The percentage of users who purchased each version is: 35% basic, 50% extended, and 15% complete. Suppose that a user who has purchased the operating system is selected at ran- dom. Let us define the following events: A: "the user consider him/herself an advanced user” B:"the user purchased the basic version”; E: "the user purchased the extended version"; C: "the user purchased the complete version"; Determine the following probabilities: (a) P(BNA) (b) P(En A) (c) P(A) (d) P(AB) (e) P(CIA) (1) P(BUA)

Answer 1

100 700 PCB = 35 P(E) = 50 P (C) = 15 100 a) P(BOA) = P(B). PlanB P (B) = P(B. P(AIB)=35x10 100 100 = 0.035 by PCENA) = P(E) - PENA) = PCC) - P(1):P(ANE) PLE) = P(E).- P(1P(ALB). - 50 - 50 40 100 100 100 - 0.3 7 P(A) = P(B).P(ATB) + P(1) P(ALE) + PL9) P(A19 = 35 100 to 100 - 50 100 40 100 15 100 80 100 =.0.355 dy P(AIB) = PLANB) = P(BRA) = P(B) - P(BRA) P(B) P(B). PLB). PIB = 1- P(BNA) P(В) =1-0.035 trom 0.35 t = 0.9 A ey P (CIA) = P(CNA) = P(G). P(ALC) - Mossel PCA) PA) 355 1000 - 20 120 355

+7 PIBUA) = P(B) + P(A) - Plena) 35 355 35 1000 = 0.67