I've seen scholars estimate 5 to 10 percent literacy in the ancient world, in general. Depending on who we count, the Gospels name anywhere from 20 to 40 specific persons who were associated with Jesus' movement during his public ministry. How many of them should we expect to be readers and/or writers? The same 5 to 10 percent? Maaaaybe...
Statistically, we might expect 1 to 4 literate persons, out of 20 to 40. Or perhaps the numbers should skew high, because certain ones among these persons were notable to begin with. Or perhaps that high skewing should balance out because the twelve were said to be "uneducated". (Though uneducated does not mean illiterate.)
To get specific, there are reasons to doubt that certain ones were literate, and reasons to believe that certain other ones were very literate. Peter? Probably not so much. Nicodemus? Oh, yes, we should think definitely. And so on. But after all the educated guesswork, the statistical question remains. Out of those 30-ish persons, how many should we consider likely to have been capable of reading and/or writing?
Moving beyond the persons actually named, what percent of the 120 were literate? Five percent nets us six literate persons. Ten gets us twelve. Of course, the ability to write doesn't mean they all spent time writing, much less took the effort to work out and put down an elaborate composition, much less 'publish' anything. But then again, it only takes one person of those 120 to have made such efforts, to give us an early written source from within Jesus' circle itself. I'd like to say these statistics alone suggest this is far more likely than not.
And remember, one hundred percent of Jesus' Jewish followers were used to being listeners. The culture was 100% literate when you include passive participation in aural recitation. It's impossible for me to imagine the 120 growing up in synagogues with their critical emphasis on hearing the word read aloud... and then think that *all* 119 of them didn't demand of at least one writer among them that he sit down and record something about Jesus' words and deeds, so they could keep it to hear read aloud, from time to time, in their own lifetimes.
It only takes ONE person to feel the need strongly enough to start badgering ONE literate person to get the job done. Again, the statistics of that seem more likely than not, by far, at least to me.
But hey. Officially, I'm somewhat uneducated. So what do y'all think? ;-)