The probability that the dog barks can be found by considering two scenarios: when they go to the park and when they do not.

1. Probability they go to the park and the dog barks:

\(P(\text{park, bark}) = 0.6 \times 0.35 = 0.21\)

2. Probability they do not go to the park and the dog barks:

\(P(\text{not park, bark}) = 0.4 \times 0.75 = 0.3\)

3. Total probability that the dog barks:

\(P(\text{bark}) = P(\text{park, bark}) + P(\text{not park, bark}) = 0.21 + 0.3 = 0.51\)