Solution1: Randomly test two keys from keys, so that the total number of sample points in sample space a is 

= .

To open the door, at least one of the two keys taken out must be obtained from the three keys that can open the door. According to the addition principle and the multiplication principle , the number of sample points contained in the event "can open the door" is 

.

According to the classical concept , the required probability is 

.

Solution2: Randomly test two keys from keys, so that the total number of sample points in sample space is 

.

Note that event is "can open the door" , then its opposite event is "cannot open the door" . Take any two keys from the keys that cannot open the door. There are ways to take it, that is, event contains a total of keys. sample points, so, according to property 3 of probability, we can get

.