A$.2$ 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 $\backslash (\backslash$tau$=50\backslash$mathrm$\{$ps$\},$ T$\_\{0\}=60\backslash$mathrm$\{$ps$\}\backslash ),$ and $\backslash ($ t$\_\{\backslash$text $\{$setup $\}\}=25\backslash$mathrm$\{$ps$\}\backslash ).$ 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$?$