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

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Question 1157441: If 3 regular six-sided dice are rolled, compute the probability of rolling a sum
that is prime and less than 11.
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
 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
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Prime numbers less than 11 that can be the sum of the numbers on three dice: 3, 5, and 7.

3: 1,1,1 1 way

5: 1,1,3 3 ways
5: 1,2,2 3 ways
7: 1,1,5 3 ways
7: 1,2,4 6 ways
7: 1,3,3 3 ways
7: 2,2,3 3 ways

Total: 22 ways

There are 6*6*6=216 different possible outcomes for the three dice; the desired probability is 22/216.

Simplify the fraction or convert to decimal if required.
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