Let:
D₁ = probability of default by firm 1 and
D₂ = probability of default by firm 2
ρ₁₂ = correlation of defaults

The Joint probability of default is given by:

$$P(D_1 D_2) = D_1 \times D_2 + \rho_{12} \times \sqrt{D_1(1 - D_1)} \sqrt{D_2(1 - D_2)}$$

Since the defaults are correlated,

$$P(D_1 D_2) = 5\% \times 1\% + 0.2 \times \sqrt{5\%(1 - 5\%)} \sqrt{1\%(1 - 1\%)} \approx 0.484\%$$

N/B: If the defaults were uncorrelated,
i.e., ρ₁₂ = 0

$$P(D_1 D_2) = 5\% \times 1\% = 0.05\%$$

This means that the joint probability of default for correlated defaults is nearly 10 times higher than the one for uncorrelated defaults.