Carl Reiner, as the interviewer, sets the scene, saying, "A plane landed at Idlewild." So, the sound track was probably taken from the recording released in 1961. JFK was still alive; his family were not naming things after him yet. So, the airport was still Idlewild, not Kennedy.
According to sources who have asked to remain nameless, citing their need to keep their real ages a secret, Mel Brooks, the 2000 Year Old Man himself, and Carl Reiner performed this little interview throughout the 1950s, but never recorded it.
I seem to remember reading somewhere, perhaps in The New Yorker Magazine, that the first recording took place at Reiner's home, sometime in the late 1950s. After dinner, Reiner turned on the tape recorder, walked the microphone over to Brooks a dear friend and guest and set the scene. Then he asked the first question...
I had the impression that the challenge was a new one for Brooks, but if my sources are correct, and they did predict that there would be no weapons of mass destruction, Brooks and Reiner had been through the routine many times before that fateful night.
Now, I have to ask, was that tape transcribed onto the record, or did the duo do it again for vinyl? I suspect they recorded it a few times. The reason is in a detail. In the review that appeared in The New York Times in 1975, when the animation on this video was first broadcast on the CBS television network, there is a quote: "I have 25,000 children...and not one of them ever writes!" In the video the quote is "I have 42,000 children ... and does even one of them ever come over to visit?" So, perhaps by the time Media Home Entertainment picked up the animation and marketed the version I have, in 1984, something changed. Who knows? Both versions of the joke are funny, unless you are sitting at home, in the dark, waiting for your kids to call or come over, in which case neither version is funny.
But seriously, "Tragedy is when I cut my finger. Comedy is when you don't look where you are going, fall in a hole, and die." Now, that's funny.