For the benefit of those not familiar with dominoes, a domino has two sides, each with a number from 0 to 6. A set consists of one of each possible domino. That would be all combin(7,2)=21 ways to choose numbers, without replacement, out of 7, plus all 7 ways to have both numbers on the same side.
Here are all all 28 of them: 0-0, 0-1, 0-2, 0-3, 0-4, 0-5, 0-6, 1-1, 1-2, 1-3, 1-4, 1-5, 1-6, 2-2-2, 2-3, 2-4, 2-5, 2-6, 3-3, 3-4, 3-5, 3-6, 4-4, 4-5, 4-6, 5-5, 5-6, 6-6.
With that explanation out of the way, here are the answer and solution.
Answer
1/4 = 25%
Solution
A simple way to reword the question is what is the probability a randomly chosen domino has the same number on both sides. That answer is simply 7/28 = 1/4.
You might say, the answer should be 1/7, because the other side could be any of the seven possible numbers. It's true it could be any of the seven numbers, but they are not all equally likely. The 6-6 domino should be double counted, because it has two sides with a six. So, the other side could be either of two sixes and there are eight total sixes in the set. Thus the answer is 2/8 = 1/4.
This question is asked and discussed in my forum at Wizard of Vegas. The question is dedicated to the memory of Alan Mendelson.