Ansible provisioning ERROR! Using a SSH password instead of a key is not possible

Create a file ansible/ansible.cfg in your project directory (i.e. ansible.cfg in the provisioning_path on the target) with the following contents:

[defaults]
host_key_checking = false

^{provided that your Vagrant box has sshpass already installed – it’s unclear, because the error message in your question suggests it was installed (otherwise it would be “ERROR! to use the ‘ssh’ connection type with passwords, you must install the sshpass program“), but in your answer you add it explicitly (sudo apt-get install sshpass), like it was not}