Some problems that are popular on the internet are in correctly classified as paradoxes but are not paradoxes at all - they are simply problems that have answers that might seem to defy common intuition and therefore have answers that come under suspicion. These are not paradoxes

First. A true paradox is a __logical contradiction__ that CANNOT be resolved by the current axioms. Famous paradoxes that are well known include:

1) ** Russel's Paradox** involving set theory and the paradox arising from the set of all sets that do not contain themselves.

2) A more popular paradox that's been around for many years arises in the Barber Problem and asking **"**__Who shaves the Barber?"__

3) Another popular one arises from 2 statements written on opposite sides of one sheet of paper. On one side is the statement ** "The statement on the other side of this sheet paper is true" **and on the flip side is the statement

__"The statement on the other side of this sheet of paper is false"__All 3 of these are** not resolvable** and thus lead to a logical contradiction and are , in fact, true paradoxes.

On the other hand there are problems often described as paradoxes __which are not__**.**

1) ** The Birthday Problem**- what is

**? When n = 35 the probability > 80% . A surprising result to a lot of people but the answer is totally correct and therefore not a paradox.**

__P(that at least 2 people have the same birthday in a group of n people)__2) ** The False Positive Problem** which arises when a rare disease is present in the population. Percentages are given concerning the reliability of blood tests. When you calculate

**the result always turns out to be so low that it goes against popular intuition. Again, not a paradox.**

__P(you actually have the disease given that you have tested positive)__Maybe this can be an informative video.