Thinking of that Julie Andrews quote I believe professionals make mistakes just like everyone else. It's just that they can recover without a lot of outward appearance of error.
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True in a lot of endeavors. Prof. musicians in top (and mid range) symphonies generally don't make mistakes. If they "do", it may be one of interpretation, not wrong notes or counting, etc. But they have practised their instrument more hours than one can imagine. There are probably other activities/jobs that are similar--maybe someone can think of one. Nobody does this with scuba (at least I would think not).