I would like to know how to solve this problem correctly, and if there is something wrong.
The users can connect to 4 servers from 4 countries, we choose 200 users that act independently from each other and we see which servers they chose(to connect to a network). The obtained data is:
Servers : A | B | C | D Users : 100 | 20 | 30 | 50
1. Find the estimated probability that a user is going to connect to server A or B?
P(A ∪ B) = P(A) + P(B) - P(A ∩ B))
P(A ∩ B) = P(A) P(B|A)
The problem is will these formulas solve this exercice? and How??
2. We need to reject the hypothesis that the users choose a server randomly without having any preferences from any of them?(confidence level is 0.05)
H0(null hypothesis): The users choose a server randomly
P(A) = 100/200, P(B) = 20/200, P(C) = 30/200, P(D) = 50/200
H1(alternative hypothesis): The users dont choose a server randomly
P(A) ≠ 100/200, P(B) ≠ 20/200, P(C) ≠ 30/200, P(D) ≠ 50/200
U = Σ [ (Ni - Ei)2 / Ei ] ~ Chi-Square, where Ni = 100,20, 30, 50
E1 = N*P1 = 200*P(A) E2 = N*P2 = 200*P(B) ....
I just need to know if im going in the right path. I would really apreciate your help on solving this exercice.