Question

Three symmetrical and homogeneous dice are tossed simultaneously. Find the probability of event A: the total number of dots appears at 10 if we know that at least one dice has upper face 3 dots. (Sorry I'm not good at English)

Answer 1

We consider case with one 3 dot die and two 3 dot die separately.

Case I: Suppose one die has upper face 3 dots. The dots on the other two dice should add to 7. The possibilities are

Each of the above event has probability . The 3 dot die can be any one of the 3. Total ways,

So the probability of getting sum 10 with only one die with 3 dots is

Case II: Suppose 2 dice has upper face 3 dots. The dots on the third should be 4. The possibilities are

The above event has probability . The two 3 dot dice can be any two of the 3. Total ways,

So the probability of getting sum 10 with two dice with 3 dots is

Thus the required probability is the sum of the above probabilities.