Probability is often taken too seriously. When someone hears that the probability of a given event occurring is zero, the usual interpretation is that the event will never occure. In other words, it is commonly thought that an event with a probability of zero is impossible.
However, take, for instance, the set of all integers. What is the probabilty of choosing a given integer at random? Since there are an infinite number of integers and we are choosing only one, we would the calculate the probability as being 1/infinity = 0.* But this means that we have zero probability of choosing any given number. That's perplexing, because if we choose a random number from the set of integers we will have just accomplished something that has a probability of zero!
Even more perplexing, the rational numbers are a countable subset of the uncountable set of real number. (The uncountably infinite set of irrational numbers are what makes the real numbers uncountable.) In other words, there are infinitely more irrational numbers than rational numbers. That means the probabiliy of choosing a rational number at random out of the set of real numbers is zero!
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Related course: Probability
