Joining two SELECT Statements with WHERE clause

Joining two SELECT Statements with WHERE clause

I think this is probably really easy but im not practiced in SQL and dont
know much of the syntax.
Basically I got a big table with different User Complaints (represented by
a problem ID) and Timestamps that I want to graph.
The individual statements are really easy and straightforward. Example:
SELECT DATE( datetimebegin ) AS Date, COUNT( * ) AS CntProb1
FROM `problems`
WHERE problemID = "1"
GROUP BY Date, problemID;
SELECT DATE( datetimebegin ) AS Date, COUNT( * ) AS CntProb2
FROM `problems`
WHERE problemID = "2"
GROUP BY Date, problemID;
Each Table gives me a pretty simple output:
Date, Prob1
2013-03-11,4
2013-03-14,1
2013-03-17,7
Date, Prob2
2013-03-12,2
2013-03-13,1
2013-03-14,3
2013-03-17,1
I need the result combined like this:
Date, CntProb1, CntProb2
2013-03-11,4,0
2013-03-12,0,2
2013-03-13,0,1
2013-03-14,1,3
2013-03-17,7,1
I guess this is something really simple if you know the right SQL
Syntax... Some kind of Join?!
Any help is really appreciated!