In mid$-2009,$ Rite Aid had CCC$-$rated, $6-$year bonds outstanding with a yield to maturity of $17\mathrm{.}3\%.$ At the time, similar maturity Treasuries had a yield of $3\%.$ Suppose the market risk premium is $5\%$ and you believe Rite Aid$$s bonds have a beta of $0\mathrm{.}31.$ The expected loss rate of these bonds in the event of default is $60\%.$

a$.$What annual probability of default would be consistent with the yield to maturity of these bonds in mid$-2009?$

b$.$In mid$-2012,$ Rite$-$Aid$$s bonds had a yield of $8\mathrm{.}3\%,$ while similar maturity Treasuries had a yield of $1\%.$ What probability of default would you estimate now?