Error probability UART RS232

Is that meant to be the probability that a valid async character will treated as an error, or that random noise will be treated as a valid character?

A UART clock is likely to be 4 times the baud, and the middle 2 clocks of each bit time can be compared for equality - giving 10 bit pairs that must match per character.

Except that the both samples of the stop bit must be zero, and the start bit (probably) has to last 3 samples. OTOH if your clock is slow you may not want to wait for all the stop bit (to avoid missing the next start bit).

Or, a different sum. At 115k, a 4x clock is 460k, to guarantee a 1% (or better) clock you'll need to divide down from 50x460k or 23MHz.

You need a 2.5% error on a 4x clock to get one clock out before the end of an async char - so 1% should be plenty! I suspect some standard will quote a closes tolerance though - it all depends on the way the UART logic is defined.