I would like to add a RGB led strip to my arduino alarm system
An interesting problem with the Arduino paradigm is that not only do you need basic programming knowledge but you also need basic electronics knowledge.

On the plus side, there are plenty of good tutorials where you can over look these issues if you follow the tutorials step by step.  That is, get exactly the same parts and wire them up exactly the same way.  Later, if you like, you can go over the tutorial, ask questions here and discover how and why what you did works.

In your diagram:

You are implying you are using ordinary Red, Green &amp; Blue LEDs and are going to vary their brightness using the Arduino's Pulse Width Modulation feature.

Possible problems:

You are powering the LEDs from the 9 volt pin of the Arduino.  And the LED strip in the diagram is clearly marked 12 volts.  This may work.  But is out of specification. 

Also, this setup makes the assumption you are powering your Arduino with a 9 volt wall power supply.  Are you?  You could also power the Arduino with 5 volts using only the USB cable.  There would then be no 9 volts available at the 9 volt pin.  (I would avoid plugging in both power sources at the same time.  I think the Arduino design has changed over time.)

You are using a strip of Red, Green &amp; Blue LEDs.  Which implies more than 1 of these Red, Green &amp; Blue LEDs.  There is an upper current limit on the outputs of the Arduino.  More LEDs means more current.  Too many LEDs will damage the Arduino.  I would stick to 1 LED until you research the amount of current 1 LED takes verses the upper current limit of an Arduino output pin.