A pencil case holds 7 blue pens and 5 black pens…

Step 1. Both blue. $\dfrac{7}{12} \times \dfrac{6}{11} = \dfrac{42}{132} = \dfrac{7}{22} \approx 0.3182$.

Step 2. Different colours. Blue then black is $\dfrac{7}{12} \times \dfrac{5}{11}$. Black then blue is $\dfrac{5}{12} \times \dfrac{7}{11}$. They are equal, so the sum is $\dfrac{70}{132} = \dfrac{35}{66} \approx 0.5303$.

Step 3. At least one black. This is the complement of both blue: $1 - \dfrac{7}{22} = \dfrac{15}{22} \approx 0.6818$.