Run a Docker container with Ubuntu:

docker run -it ubuntu /bin/bash

Then try a ping:

ping somesite.com
bash: ping: command not found

Docker images are pretty minimal, but you can install ping in the official Ubuntu docker image via:

apt-get update
apt-get install iputils-ping

But if you need ping to exist on your image, you can create a Dockerfile or commit the container you ran the above commands in to a new image.

Commit:

docker commit -m "Installed iputils-ping" --author "Your Name <name@domain.com>" ContainerNameOrId yourrepository/imagename:tag

Dockerfile:

Dockerfile

FROM ubuntu
RUN apt-get update && apt-get install -y iputils-ping
CMD bash

Please note there are best practices on creating docker images, Like clearing apt cache files after etc.

apt-get fails with Temporary failure resolving 'security.ubuntu.com' obviously because networking is not present.

mkdir ubuntu_with_ping
cat >ubuntu_with_ping/Dockerfile <<'EOF'
FROM ubuntu
RUN apt-get update && apt-get install -y iputils-ping
CMD bash
EOF
docker build -t ubuntu_with_ping ubuntu_with_ping
docker run -it ubuntu_with_ping