Suppose a 3-year corporate bond provides a coupon of 7% per year payable semiannually and has a yield of 5% (expressed with semiannual compounding). The yields for all maturities on risk-free bonds is 4% per annum (expressed with semiannual compounding). Assume that defaults can take place every 6 months (immediately before a coupon payment)

and the recovery rate is 45%. Estimate the default probabilities, assuming

(a) that the unconditional default probabilities are the same on each possible default date and

(b) that the default probabilities conditional on no earlier default are the same on each possible default date.