Random coincidences of life, or how did it happen that at the tractor factory you were presented with a cake

“Coincidence” is a case that seems very unlikely to us, but it still happens.

Have you met "coincidences" in your life? In the parking lot, three red cars are nearby, your friend put on the meeting exactly the same T-shirt, the room with a beautiful view was the only free one, and the computer turned off at the moment when the guests had to open the door. We encounter situations that are very unlikely in themselves. And indeed, let's see how likely my two Nissan Skyline units will stop at my house? Even if there are 10,000 cars in total, and only two Nissan Skyline are among them, then the probability is negligible:

$$

$$\ frac {2!} {10000 ^ 2}$$

Every time we are surprised at such "coincidences", but is it so unlikely? We will understand.

To begin with, we introduce the concept of “fixing an event”. This means that before conducting the experiment (that is, before we look at the parking lot at my house) we write on a piece of paper which particular pair of cars we want to see.

Suppose there are two parallel universes. In each of them you sit at home and are going to go to a cafe:

In the first one you go and notice on the road: at the traffic lights there are two identical trucks, and in the cafe two people are celebrating their birthday at once.

Surprisingly, these coincidences are so unlikely!

In the second, you are asked to first fix the events - try to predict "coincidences". You go to a cafe and watch what is happening.
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In the first case, the probability is high, you notice all the random "coincidences".

And in the second, the probability of these events is really small: after all, you recorded only a few "coincidences". Most likely you will not meet "coincidences" at all.

I explain by example.

We will transform our universe into a parking for cars, and the space of events into “coincidences” of car pairs, that is, into many coincidences of car models.




Now go through the track without fixing the event. What is the probability that we will see two identical cars standing next to each other? Pretty big.


What was in the spoiler: we noticed that if you walk along the path in search of the same pair of cars, we will find it with a probability of more than 63%. But if you first think up where and what cars are located, then the probability of an event will be less than one half million.

Now back to real life. As in the parking lot there were many different possible cases, so in our world the colors of the fur of neighboring cats may coincide, the letters of the car numbers at the traffic lights, a scholarship given at the right time.

Conclusion: in spite of the fact that the probability of each individual “coincidence” is extremely small, the probability that at least some “coincidence” will occur is rather large. At our parking lot, we waited for at least some “coincidence”, and since we didn’t care about the model of cars or where the pair was located, the probability was high. But if you recorded an event before leaving home, then the probability of meeting a “coincidence” is already very small. But you, of course, did not reduce the likelihood of this event, you just stopped taking into account the rest .

So do not be surprised when you are suddenly given a cake at work. Because you would not care anyway expressed sympathy.