The probability that Melania Trump did NOT plagiarize from Michelle Obama's 2008 Democratic National Convention speech is about 1 in 87 billion; 0.0000000000115%.
Melania Trump's speech transcript can be found HERE.
Text Fixer gives a word count of 1372 words for the transcript, and 109 words for the allegedly plagiarized portion.
That's 12.59%... at most, as it depends on how many of the words one includes from the excerpt. I sought the maximum, hence included the whole excerpt.
Melania Trump's:
My parents impressed on me the values: that you work hard for what you want in life. That your word is your bond and you do what you say and keep your promise. That you treat people with respect. They taught me to show the values and morals in my daily life. That is the lesson that I continue to pass along to our son. And we need to pass those lessons on to the many generations to follow. Because we want our children in this nation to know that the only limit to your achievements is the strength of your dreams and your willingness to work for them.
Michelle Obama's:
And Barack and I were raised with so many of the same values: that you work hard for what you want in life; that your word is your bond and you do what you say you're going to do; that you treat people with dignity and respect, even if you don't know them, and even if you don't agree with them. And Barack and I set out to build lives guided by these values, and pass them on to the next generation. Because we want our children — and all children in this nation — to know that the only limit to the height of your achievements is the reach of your dreams and your willingness to work for them.
HERE are a few theories behind the situation.
Here is the word frequency chart for the whole transcript (obtained from Text Fixer):
