Faced with almost an infinity of details you cannot afford to deal constantly with the specific; you must learn to embrace more and more detail under… - Richard Hamming

Statistics should be taught early so that the concepts are absorbed by the student's flexible, adaptable mind before it is too late.

I need to discuss science vs. engineering. Put glibly:
In science if you know what you are doing you should not be doing it.
In engineering if you do not know what you are doing you should not be doing it.

Probability plays a central role in many fields, from quantum mechanics to information theory, and even older fields use probability now that the presence of "noise" is officially admitted. The newer aspects of many fields start with the admission of uncertainty.