A$\mathrm{.}2$ Synchronizer MTBF

You are designing a synchronizer circuit that receive an asynchronous inputs. Your goal is to have an

MTBF of $5$ years. The asynchronous input is expected to change once have $0\mathrm{.}1$ second. You are building

the synchronizer using a sampling flip$-$flop with $=50$ ps$,$ T$0=60$ ps$,$ and tsetup $=25$ ps$.$ Answer the

following:

$1.$ What is the required probability of failure to satisfy this MTBF$?$

$2.$ How many clock cycles do you need to wait before reading the sampled input to ensure a probability

of error that satisfy the above MTBF$?$