##### 1. The drinker paradox

This paradox is best to be reflected upon on Friday evening at a bar, which can create the appropriate mood. It is formulated as follows: ** “In any pub, there is someone such that if he is drinking, then everyone in the pub is drinking.“** The logic is as follows:

A) Let’s say it’s true that everyone is drinking in the pub. Let’s isolate one person from all local drunks, for example, Jack. Then, if they all are drinking, Jack will be drinking also. And vice versa.

B) The second option is has it that not everyone is drinking in the pub. Then only one person remains sober, let it be Jack again. Since it is incorrect to say that he is drinking, it is safe to say that when he is, everyone else is drinking also.

From the point of view of common sense these claims more than far-fetched. But according to the rules of scientific logic they work. Firstly, a false statement could lead to any conclusion. Secondly, the fact that Jack is drinking is a false statement when we say that if he is drinking, everyone else is drinking also, which is also a false statement. Hence, the total conditional statement is true.

##### 2. The paradox of the liar

One of the oldest and most popular paradoxes has many statements: *“I am lying”, “This statement is a lie,”* and even *«Everybody lies»*. According to the legend, this paradox which is favored by **Gregory House**, belongs to a Cretan by the name of **Epimenides**, who believed that all Cretans were liars, the statement which puzzled philosophers for a long time.

If *«Everybody lies»* is a true statement, it means that even Mr. House lies. So the statement carrying a message that everyone lies is itself a lie, and it contradicts the content of the statement. Conversely, if the statement is false, House is telling the truth.

##### 3. The elevator paradox

The paradox is in that when you are located on **one of the upper floors,** the elevator often comes to you **from the bottom**. And if you happen to be on the **second or third floor**, the elevator arrives** from the top** more frequently. This strange pattern was once noticed by the physicists **George Gamow and Marvin Stern**, who worked on different floors of a building. What’s the explanation? Many scientists, together with Gamow and Stern, tried to find an explanation for this strange phenomenon. Here is the most probable explanation.

For a person who is located on the top floor, all the elevators, of course, will arrive from below, and then go down again. For passengers located on the floor before the top floor, first will arrive the elevator that is going to the top floor, and it will be going to the bottom floor a bit later. It turns out that the “top-floor passengers” will first get the elevator going up. The same situation occurs with the lower floors.

##### 4. Player’s Mistake

The intuitive perception of the events probability can contradict **the Probability Theory**. In fact, oddly enough, the probability of the desired outcome of a random event is not affected by previous outcomes.

For example, suppose you toss a coin, and you get 10 heads in a row. It seems that next time you will get tails, but the probability of getting heads from your toss is still, paradoxically, 50%.

##### 5. The murdered grandfather paradox

Let’s say a guy named Tom went back in time and killed his own grandfather before the grandfather had a chance to meet the grandmother. As a result, neither Tom’s parents nor Tom himself were born. This means Tom would not be able to travel back in time, which means that he did not kill his grandfather, the grandfather still lived, and so did Tom was born, and … this cycle of events can be repeated indefinitely…

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#### Anna LeMind

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paradox no 4…— 0nly 50% chance holds in cases of classical probability theory. not in the advanced theories of probability…

The Player’s Mistake is a classic. It’s also applicable to dice (e.g. no matter how many time you roll a 6, the chances of it taking place at your next roll is still 16.7%), as well as the roulette and several other games of chances. The only exception is card games, where the probabilities change as the deck grows slimmer.

In the Drinker’s Paradox, we get messed up by what amounts to an existential quantifier on an implication — a logical construct that is almost never seen in mathematics, for good reasons.

An “non-paradoxical” but related scenario would be as follows: In any pub with two or more people in it, it can be shown that it is possible that one person is drinking and not everyone else is drinking. (The proof requires only a bit of set theory.)