To forcefully remove a Docker image with the name 'mistake:v1', the correct command is 'docker rmi -f mistake:v1'. This command deletes the image even if there are existing containers that depend on it.
The command to remove the image called 'mistake:v1' from the local system even if there are containers based on it is b) docker rmi -f mistake:v1. The '-f' option stands for 'force', which tells Docker to remove the image even if there are stopped containers that were based on that image.
It's important to use this command with caution, as forcing the removal of an image with dependencies can lead to data loss if those containers have not been properly backed up or if you need to preserve their current state.