Mary Williams was born in Llanfairfechan, Carnarfonshire, Wales about 1883. She is the daughter of John Williams and Alice Abram.
In 1901 the Census lists her at 18 years old in the household of her mother (a widow) and some siblings. 
↑ "England and Wales Census, 1901," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:X9BC-Z8P : 21 May 2019), Mary Williams in household of Alice Williams, Llanfairfechan, Caernarfonshire, Wales, United Kingdom; from "1901 England, Scotland and Wales census," database and images, findmypast (http://www.findmypast.com : n.d.); citing Llanfair-Fechan subdistrict, PRO RG 13, The National Archives, Kew, Surrey.
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It may be possible to confirm family relationships with Mary by comparing test results with other carriers of her ancestors' mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage (beta) of DNA with Mary: