[request] Domino probability questions

My son is curious about probabilities but it is way over my head. He’s trying to figure out odds of getting certain dominos in a set of 91. He’s worked it out with some double checking from ChatGPT but was hoping someone could verify. Here’s his thinking:

In the game dominos, you would have a 1.1% chance of getting any one particular domino from the domino box. But if you wanted to get that same domino from the starting hand (15 dominos) you would have a 16.5% chance to get the domino you wanted, because you have 15 chances to get the domino.

If you wanted a domino with double of the same number on each side, you would have a 14.2% chance of getting the domino you wanted, because having thirteen of those dominos makes you have a higher chance. If you wanted to get a double from your starting hand, you would have a 95.8% chance to get a double numbered domino because there are thirteen double numbered dominos, you have a much higher chance of getting it.

also, all of this is assuming nobody else is playing and the box of dominos has 91 dominos inside.