SOLUTION: If 3 regular six-sided dice are rolled, compute the probability of rolling a sum that is prime and less than 11.

 1.  (1,1,1) has sum 3, which is prime and less than 11.
 2.  (1,1,3) has sum 5, which is prime and less than 11.
 3.  (1,2,2) has sum 5, which is prime and less than 11.
 4.  (1,3,1) has sum 5, which is prime and less than 11.
 5.  (2,1,2) has sum 5, which is prime and less than 11.
 6.  (2,2,1) has sum 5, which is prime and less than 11. 
 7.  (3,1,1) has sum 5, which is prime and less than 11.
 8.  (1,1,5) has sum 7, which is prime and less than 11.
 9.  (1,2,4) has sum 7, which is prime and less than 11.
10.  (1,3,3) has sum 7, which is prime and less than 11.
11.  (1,4,2) has sum 7, which is prime and less than 11.
12.  (1,5,1) has sum 7, which is prime and less than 11.
13.  (2,1,4) has sum 7, which is prime and less than 11.
14.  (2,2,3) has sum 7, which is prime and less than 11.
15.  (2,3,2) has sum 7, which is prime and less than 11.
16.  (2,4,1) has sum 7, which is prime and less than 11.
17.  (3,1,3) has sum 7, which is prime and less than 11.
18.  (3,2,2) has sum 7, which is prime and less than 11.
19.  (3,3,1) has sum 7, which is prime and less than 11.
20.  (4,1,2) has sum 7, which is prime and less than 11.
21.  (4,2,1) has sum 7, which is prime and less than 11.
22.  (5,1,1) has sum 7, which is prime and less than 11.

So there are 22 such rolls out of 6∙6∙6 = 216 rolls.

So the probability = 22/216 = 11/108 or about 10.1% of the time.

Edwin