Consider Two Firms with One-Year Probabilities of Default Of $$p _ { 1 } = 0.10$$

Consider two firms with one-year probabilities of default of $$p _ { 1 } = 0.10$$ and $$p _ { 2 } = 0.05$$ ,respectively.The correlation of default of the two firms is $$\rho = 0.5$$ .What is the conditional probability of default $$\operatorname { Pr } \left[ D _ { 2 } \mid D _ { 1 } \right]$$ ?

A) 0.38
B) 0.42
C) 0.46
D) 0.50