The fundamental mathematical concept employed in understanding such randomness is probability.

基本的数学概念的理解，例如采用随机性的概率。

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Using properly counterexamples in the teaching of Probability Theory will help students have a good understanding of the course, warm up their active thinking and improve teaching quality.

在概率论教学中，恰当的运用反例教学，可以帮助学生加深对该课程的理解，并激发他们积极思维，有助于提高教学质量。

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In a series of problem in probability calculation need for understanding the signification of integral variable and using graphical representation as an assistant tool.

在概率的一系列计算问题中，需要准确认识积分中变量的意义和利用图示作为辅助工具。

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Also, anybody with a basic understanding of probability can prove mistakes are unlikely to even themselves out.

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Understanding the probability for success and knowing what a fair payout is are critical when playing the lottery or selecting mutual funds.

FORBES: Possible Isn't Probable in the Lottery or Investing

In this we see the genius of the entire book: Silver is able to appeal to those who are both mathematically and non-mathematically inclined, building a compelling story as to why both types of reader should be interested in the better quantification and understanding of the probability of the events that surround us every day.

FORBES: A Guide to Thinking In the Era of Big Data: Nate Silver's "The Signal & The Noise"