As @ydaetskcoR said, you're missing Ansible on the host machine. Alternatively, you can run the playbooks locally, but the provisioner that ships with Vagrant doesn't support that, so you'll have to do it with a shell provisioner:
config.vm.synced_folder "ansible", "/opt/ansible"
config.vm.provision "ansible", type: "shell" do |s|
s.inline = <<SCRIPT
hash ansible-playbook &> /dev/null
if [ $? -eq 0 ]; then
echo Ansible already installed.
else
echo $(date +"%T"): Updating APT database.
apt-get update &> /dev/null
echo $(date +"%T"): Installing Python and pip.
apt-get -y install python-pip python-dev &> /dev/null
echo $(date +"%T"): Installing Ansible via pip.
pip install ansible &> /dev/null
fi
mkdir -p /etc/ansible
hostname > /etc/ansible/hosts
echo $(date +"%T"): Executing Ansible playbook.
ansible-playbook /opt/ansible/playbook.yml --connection=local
SCRIPT
end