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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While understanding your enemy may well lead you to agree with him, it also gives you more ammunition against him as well as a higher probability of reaching a compromise.

如果说理解你的敌人有可能会使你同意他们的观点，这也会同时给予你更强大的火力与他们作战和更高的几率与他们达成妥协。

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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"