1940 U.S. Census: What's that about probability?

I've indexed 137 pages of 1940 U.S. Census records from New York State and now the unthinkable has happened: I found a relative while indexing.

Last evening I electronically requested a batch to index. I selected New York State and waited a few seconds until the page popped up on my screen: Bronx ED 3-956, page 8B.  As sometimes happens, the first record only indicated a first name with neither surname nor household number: Sandra. As I have so many times since early April when I first started indexing, I looked at the prior census page to see the information from Sandra's family so I could enter her information correctly. Household 136.  Max, Fanny, and Anita Buchman. [gulp!] My great aunt and uncle and their daughters (my first cousins once removed).

Fanny Garber Buchman was my grandfather's youngest sister.  We knew her as Aunt Feigah.

The Buchman family lived at 1262 Boynton Avenue, Bronx, New York. The rented their apartment for $37 per month. The circle with the X next to her name indicates that Fannie was the informant for the Census enumerator.

Max and Fannie (she spelled her name as "Fannie" on most documents in my possession) were 38 and 36 years old, respectively. Max is recorded as having studied 7 years in school and Fannie, I think, 1.

They both emigrated from the Russian Empire and Max had become a citizen. He, in fact, was naturalized on 6 June 1927.[1]  Fanny didn't naturalize until 1952 when she still lived at this address.[2]

Columns 26-32 indicate that Max worked 44 hours during the week of March 24-30, 1940 as a salesman in the retail dress business. For this he earned $2080 per year. Fannie worked at home.

1262 Boynton Ave, Bronx, NY in 2012 (from Google Maps)

Anita was 11 and Sandra 4 on April 1, 1940.  Anita had completed sixth grade and Sandra had yet to attend school.

I had actually already located the Buchman family record several weeks ago in 1940 U.S. Census independent of this surprise. I'd determined their likely address, their possible EDs and then browsed the appropriate ED pages and located the Buchmans on these pages. But, it's still pretty amazing that they popped up when least expected as I was indexing.

When batches load for indexing, the program sometimes indicates that the page one is receiving may have been partially indexed. When this occurs, it is my understanding that someone may have not completed their indexing of the page within the allotted time and the program, therefore, turned the batch over to someone else.  This was one of those cases. Makes me feel like this one was seeking me out.

Considering that there were 132 million people in the United States in 1940 and in New York, the most populous state, there were 13.5 million, this is pretty amazing.

Notes
1. "Petition for Naturalization from the U.S. District Court for the Southern District of New York, 1897-1944," digital images, Ancestry.com (http://www.ancestry.com : accessed 13 May 2012), Petition for Naturalization No. 98373, Max Buchman, 6 June 1927; citing National Archives and records Administration microfilm publication M1972.
2. "Index to Petitions for Naturalization filed in New York City, 1792-1989," U.S. District Court for the Southern District of New York, database on-line, Ancestry.com (http://www.ancestry.com : accessed 123 May 2012), Card No. 6997117, Petition No. 608951, Fannie Buchman, 16 June 1952; citing National Archives and Records Administration, Northeast Region.