How do you explain a p-value to non-statistician collaborators?

I keep running into the same problem when working with biologists and clinicians: they want a simple yes-or-no answer from a p-value, and my careful explanation gets lost.

I have tried analogies, worked examples, and short written notes, but the misunderstanding often comes back in the next meeting.

What has actually worked for you when explaining p-values and confidence intervals to collaborators without a statistics background?