Beginner probability question about the phrase "order doesn't matter"

We can say that the order doesn't affect the probability. Of course, father choosing then son would be a different experiment from its opposite. Father and son are just labels and do not affect the probability of the event.

If they do it simultaneously, then there are $10\times 10 = 100$ different outcomes, with $10$ where they choose the same dish. So $\frac{10}{100} = \frac{1}{10}$ of choosing the same dish, which is equivalent to $\frac{9}{10}$ of chosing different.


I don't understand what you are trying to express.

There are two seperate events: the father choose a dish, and the son choose a dish.

It doesn't matter whether they do it simutalneously, or one after the other, the probability is always $\frac9{10}$

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Probability

Conditional Probability

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