Estimate number of clients using Joint Distribution I have a server able to observe from which country a client makes a request. Then, my server gives me the distribution of clients (on a 24h basis).
Let's say that we have :
Belgium: 10%
Canada: 40%
China: 50%

Now, I know that I have a defined number of clients in two cities in each country. Let's say :
Belgium_city1: 10000
Belgium_city2: 5000
Spain_city1: 20000
Spain_city2: 15000
China_city1: 40000
China_city2: 60000

I would like to estimate the number of clients originating from each city and make a request to the server.
The solution given by my professor is to just multiply the number of clients of one city by the probability of the country where the city is located.
For Belgium_city1 as example : 10000*0.1 = 1000 clients requesting my server
But I don't understand the rationale of this solution. I tried the joint distribution like this.
Let A = client comes from Belgium
Let B = client comes from Belgium_city1

$P(A,B) = P(B|A)P(A)$
where :
P(A) = 10% as observed by the server
P(B|A) = P(Belgium_city1)/[P(Belgium_city1)+P(Belgium_city2)] = 10000/15000

Then my probability a client requests the server from Belgium_city1 is P(A, B) = 10000/15000*0.1.
Now to estimate the number of clients making requests from Belgium_city1, I'm not sure how to do it. The only way to find 1000 as my professor said is to multiply my previous probability by the total number of clients in Belgium.
But why should I have to do that? This is not clear to me. I think I should multiply by the total of clients from each country and not only Belgium.
Can someone explain where is the mistake?
Thank you in advance!

You don't really have relevant information. You have information on the distribution of traffic, but it doesn't say how many requests were made. For example, there could be 5 requests from China, 4 from Canada, and 1 from Belgium. As you can see, those numbers do not necessarily have much to do with the total number of customers. To calculate this, you would need to know $P(\text{request} \,|\, \text{country})$ rather than $P(\text{country} \,|\, \text{request})$ (what you have). You could use the Bayes theorem here, but you need additional data, like $P(\text{request})$ (the probability that a customer makes a request).
