# Probability of multiple events happening at the same time

Let say I have X amount of connections on a server per hour. Each connections last for an average of Y seconds.

What's the probability of having Z connections at the same time during this hour?

I don't know where to start, so any idea would be welcomed.

Thanks.

• I think this question is not very clear. – Lost1 Oct 31 '13 at 20:31

This is where I would start. I would first get X and Y to be similar units i.e. convert Y from average in seconds to average in hours.

Then I would multiply X and Y to eliminate hours.

From there I would divide XY by Z.

Ex.

X = 100 connections/hour

Y = 360 seconds

Z = 50 connections

Y = (360 seconds)*(1 hour/3600 sec) = 1 / 10 hours

XY = (100 connections/hour) * (1 / 10 hours) = 10 connections

XY/Z = (10 connections) / (50 connections) = .2 = 20%


This probably isn't the best solution for this problem, but in my mind this is an acceptable one. I feel like more information (i.e. standard deviation and variation) would help give a better and more accurate probability.