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Bond Default Rates

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Q. You are holding 1 unit of a zero bond issued by XYZ. The face value and the recovery rate are respectively $100 and 40%. The term to maturity is 5 years. If XYZ defaults at any time in the coming five years, the recovery rate will be paid at the maturity day. The price of the bond is $60.

a) If the bond is Ba-rated, find the probability of defaults using the table of historical default rate.

b) Suppose a four-year zero coupon US treasury bond with face value of $100 is selling at $93, what would be the default probability of the junk bond implied from the market price?

c) Using each of the probabilities obtained from a) & b) calculate the expected value and variance of your credit loss.

I got 10.453% - 8.146% = 2.307% for part a) but I'm unsure if its correct. Also not sure how to do parts b and c. Any help is appreciated!
 
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