Independent events occurring simultaneously

#1
Hey guys,

I saw a similar question on the site, but still need some help with my own. Here it is:

Consider a double computer intruder detection system with system A and system B. If there is an intruder, system A sounds an alarm with probability .95 and system B sounds an alarm with probability .85. If there is no intruder, system A sounds a false alarm with probability .2, and system B sounds a false alarm with a probability of .1. Now, assume that the probability of an intruder is .4. If both systems sound an alarm, what is the probability that there is an intruder?

I've tried making a tree diagram, and messing around with equations, but I can't seem to get it.
 

Dason

Ambassador to the humans
#2
Please don't post the same thread more than once. This is more appropriate for 'Probability' so I deleted your other one.