Step 1 :Find the probability of choosing the 4: \(\frac{1}{10}\)
Step 2 :Given that we chose the 4, find the probability of choosing an even number: \(\frac{4}{9}\)
Step 3 :Multiply the probabilities: \(\frac{1}{10} \times \frac{4}{9} = \boxed{\frac{2}{45}}\)