no problem

is recorded from the 1960s as an informal reply of assurance. The English playwright John Osborne missed the point (perhaps deliberately) when he wrote two years before his death:

Last week, on doctor's orders, I telephoned a pathology factory to organise a blood test. 'No problem.' How can they possibly know until I've had it? But I do hope they're right—Spectator, 1992.

It was the organization of the blood test, and not its outcome, that (at that stage at least) presented no problem, idiomatically if not actually.

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