Explanations for coincidences include concordance.
In her speech on July 19, 2016 at the Republican National Convention, Melania Trump echoed the words of Michelle Obama in her 2008 speech at the Democratic National Convention. The parallels drew complaints of plagiarism and worse. Others asserted that this was “just a coincidence.”
There is a third alternative: concordance. Concordance refers to the likelihood that two people with many similarities may think the same thoughts.
Evidence for concordance comes from a study of identical twins. Examining the possibility of telepathy in twins, Blackmore and Chamberlain presented 6 pairs of twins (3 identical, 3 non-identical) ages 11-20 with several challenges. One of them was a number test. Each twin pair (and the 6 pairs of sibling controls) were asked to write down a number between 1-10 and concentrate on the number. The receiver, in another room, was asked to concentrate and guess which number the sibling had selected.
In the second part of the experiment, the researcher selected the number. The hit rates were much higher when the twin selected the number than when the researcher did. Similarly with a drawing test and picture test. The twins like certain numbers and certain images. Twins are more likely to select the same number or image because they have been raised together and have very similar genetic predispositions.
The so-called "demand characteristics" of the situation most likely contributed to the parallels between Michelle and Melania. The term "demand characteristics" originated within psychological research where researchers noticed that subjects changed their behavior to fit their ideas about what the experimenter wanted from them.
This important observation generalizes to the perceived social demands of many other situations. Being the wife of a the presidential candidate at a major political convention most likely shaped the parallels in the women's speeches. This Melania-Michelle parallel is not "just" a coincidence and most likely not plagiarism. Coincidences generally have multiple explanations. Like the twins, these two women found themselves in very similar situations and reacted similarly.