What is ARPA, Probing in internet, Ping

Tell me about the following:
1 - what is ARPA and whats is work?
2 - what is "probing the internet"?
3 - what is problem with "PING"?

ARPANET was the network that became the basis for the Internet. Based on a concept first published in 1967, ARPANET was developed under the direction of the U.S. Advanced Research Projects Agency (ARPA).

Probing the Internet means to examine the Internet. Ping is a protocol for testing whether a particular computer is connected to the Internet/LAN by sending a packet to its IP address and waiting for a response. Ping command is used to know whether certain computer is connected to network or not.

Ping cannot tell the reason of problem