Synonymous idiom for "A stopped clock is right twice a day"

Solution 1:

Wiktionary suggests:

even a blind pig can find an acorn once in a while

and:

Even a blind squirrel finds a nut once in a while: This expression means that even if people are ineffective or misguided, sometimes they can still be correct just by being lucky.

(English-for-students)

These idiomatic expressions which involve animals appear to have a Latin origin:

If you’re having a tough time finding something, remember that even a blind pig can find an acorn once in a while. This encouraging idiom actually comes from ancient Rome, where the concept of a blind animal turning something up lent itself to the Latin saying that a blind dove sometimes finds a pea. An 18th-century Friedrich Schiller play employed the blind-pig-and-acorn version, and the play’s translation into English and French may have brought it into modern English speech.

(www.waywordradio.org)

Solution 2:

every dog has its day:

Even the least fortunate person will have success at some point.

I know you're shocked that that dopey kid got a better grade than you, but hey, every dog has its day.

Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.

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Every dog has its day. and Every dog has his day.

Even the lowliest will sometimes come to the fore, as in

They may not listen to me now, but just wait, every dog has its day.

This proverbial saying alludes to the lowly status dogs once held. [Mid-1500s]

The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 2003, 1997 by The Christine Ammer 1992 Trust.

Solution 3:

If you had an infinite number of monkeys with an infinite amount of typewriters, eventually...