Claims that 40% of all firearm transfers are private sales

The "40 to 50%" of people Mayor Bloomberg, the Brady Center and many other anti-gun groups glibly say bypass background checks is misleading fiction and pure propaganda. The original study, done by the Department of Justice years ago, is faulty since it was based on an extremely small sample size using telephone questions to ask a few random people who were willing to answer questions about their guns over the phone to an unknown person (how many declined to respond???), who had no obligation to tell the truth, then relied on memory. Nevertheless, the percentages are revealing.

66% Through a dealer (Gun shop, Pawn shop, and other dealers)
4% Gun show or flea market (Dealers sell at gun shows and require background checks)
3% "Through the mail" (Requires delivery through a licensed dealer and would require a background check)
12% Member of the family (includes gifts, purchase, theft...)
13% Friend or acquaintance (includes gifts, purchase, theft...)
3% Other

According to the study, 35% at the most, may have been purchased without a background check, but many of those categories may have required a background check.

Here's the source (Page 5)
https://www.ncjrs.gov/pdffiles/165476.pdf

Seems the anti-gun zealots are using "percentage creep". From what I see, they started saying "nearly 40%", then 40% and now "nearly 50%". The DOJ report belies those claims - even though the report is fatally flawed. For example, would I (or any other sane person) respond to some anonymous voice over the phone asking about my guns? In the infamous words of William Newell (of Fast and Furious), "Hell, No!".

Requiring a universal background check on all transfers would be a legal nightmare. Every father who gives his son or daughter a .22 rifle at Christmas would be in violation. Every man who buys his wife a defensive handgun would also be in violation. Inherit your father's gun collection, and you're in violation. Find an old gun in the attic of a house you bought, and you're in violation.... And so on into absurdity.

And I will add to this John Fund article, the study was done before the Clinton Administration clamped down on Kitchen table FFL owners in the first term, cutting the number of FFL owners in the US by half. It was that cut that prompted Clinton to rein in Reno before the 1996 election to minimize the gun issue before his re-election.

When was the first time any gun owner told the truth to a phone pole.

That is why the poles say only 40% of homes have guns. The only people who would believe those poles are uninformed. Gun people don't tell polsters the truth, mostly they don't answer poles at all.