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 $\operatorname { Pr } \left[ D _ { 1 } \mid D _ { 2 } \right]$ ?

A) 0.55
B) 0.65
C) 0.75
D) 0.85