If the rate of one$-$year government securities currently is $6$ per cent, what is the repayment probability for each of the following two securities$?$ Assume that if the loan is defaulted, no payments are expected.$$

$($a$)$one$-$year AA$-$rated bond yielding $9\mathrm{.}5$ per cent?

$($b$)$one$-$year BB$-$rated bond yielding $13\mathrm{.}5$ per cent?