The paradox is simple to explain but it really confuses me. Suppose X is the weight of a mango from a very large batch of mangoes. Let's say X is normally distributed with mean $= 300$g, so the probability of a randomly picked mango weighing less than $300$g is $1/2$.
If you pick two mangoes at random, the probablity that both of them weigh less than 300g is $\frac{1}{2}×\frac{1}{2}=\frac{1}{4}$.
However, if you change the condition by a little and ask: If two mangoes are picked again at random, what is the probability that one weighs less than 300g and the other weighs less than 299.9999g? You have to consider the two possible orders and apply permutation. The answer would be $2×\frac{1}{2}×(\frac{1}{2} - \text{a teeny tiny amount})$ which is about $\frac{1}{2}$, almost double of $\frac{1}{4}$!
What I don't understand is that there seem to be very little difference between the two situations yet there is a huge disparity in the results. Is there something very significant about that slight change of $0.0001$g? Or does this just mean that such questions that you get from school math papers are meaningless in practice (eg. Probability of picking $2$ white balls and $1$ black ball from $20$ white and $30$ black balls)?
Thanks for any help to clarify this paradoxical situation.