1. Given a system of 10 users where any user is active 20% of the time. What is the probability that more than 5 users are active at any given time in this system? Use up to 5 decimal places precision.

Solution (Partial):

P(X>5)=1-P(X<=5)=1-P(X=0)-P(X=1)-P(X=2)-P(X=3)-P(X=4)-P(X=5)

p=0.2

1-p=0.8

P(X=1)=10C1p(1-p)^9=0.26843

P(X=2)=10C2p^2(1-p)^8=0. 0.30198

P(X=3)=10C3p^3(1-p)^7=0.20132

P(X=4)=10C4p^4(1-p)^6=0.088080

P(X=0)=10C0(0.8)^10=0.1073741824

P(X=5)=10C5(0.2)^5(0.8)^5=0.0264241152

P(X<=5)= 0.93321

P(X>5)= ?