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He stills says that the odd numbers and prime numbers can be put in one to one correspondence, and thinks it follows from this that they are equally likely to be drawn.

I like some of these examples, but while they probably show that he is wrong in his conclusion, they don't pick out the mistake in his reasoning.

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He's assuming that the cardinality of a set has something to do with the measure of a set:

Here's a (relatively simple) counterexample. Let's say we consider the interval [0,1]. Depending on what you like, we can consider the rationals, or the reals on that interval.

Now, for the usual notion of probability, the chance of the randomly chosen value being on [0,.5] is going to be .5.

However, the cardinality of [0,.5] and [0,1] are the same since division by two (or multiplying by two if you're going in the other direction) is an easy 1-1 correspondance.

As has already been pointed out, if the inference were correct, you would be equally likely to pick an odd number as *any natural number*. Moreover, from the same inference you get that any even number is equal in likelyhood to be chosen to any natural number. Since the probabilities are exclusive, this leads to the conclusion that you're twice as likely to pick a natural number as you are to pick a natural number when picking a natural number.

I said, in my inital response that neither the probabiltility of picking an odd number, nor the probability of picking a prime is well-defined, so, without more context he might as well be asking what you get if you divide the color blue by the concept of justice.