Lord777
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Random coincidences often seem magical to us, but in reality they can be explained using statistics and mathematics.
Our ideas about the random are not at all random. Hearing an amazing story, how someone ended up in the right place at the right time in a completely unpredictable way, we show sincere interest, make round eyes and begin to wonder if this is fate or the hand of the Almighty?
Randomness is not a very intuitive thing. More precisely, her perception is often intuitively wrong. Everyone knows that the probability of getting heads or tails on a correct coin is ½. At the same time, nothing prevents the coin from falling heads 10 or 100 times in a row. There is no condition that heads and tails should alternate. The coin either falls heads up or it doesn't.
Incredible coincidence or pattern?
Coincidences happen a lot more often than we think. We just don't notice them. In order to notice a coincidence, it is necessary that it has specific meaning for us.
You can do a thought experiment. Imagine being introduced to a friend at a party. After that, you meet him in a bakery, in a store, then at a bus stop at the house. Maybe this person is destined for you from above and someone in heaven arranges regular meetings for you? Or you could have seen him before in the same places, just did not attach any importance to it and paid no more attention to him than to other bystanders?
You began to notice him because he became familiar to you, this particular person acquired meaning in your world.
"The paradox of birthdays"
There is a well-known paradox. Try to roughly estimate how many people should be in a group so that two people have the same date of birth (day and month) with a probability of more than 50 percent? It seems that the number of people should be large enough. But in reality, it only takes 23 people. 23 people is less than the average school class. It turns out that in a school class, it is more likely that one of the classmates will have birthdays on one day than that everyone will have their own unique birthday.
This problem is called a paradox because of the sharp discrepancy between the intuitive and mathematically correct answers.
Why is there such a difference between perception and cold math calculation? According to our estimates, the probability of being born on a certain day is quite small, and the probability that two people will be born on the same day is even less. Therefore, it turns out that our brain gives us a small probability as an answer.
What happens when you look at this from a mathematical point of view? The fact is that the problem says about the coincidence of birthdays for any two people in the group. In this case, the probability is determined by the number of pairs of people that can be made up of 23 people. From 23 people, you can make 253 unique pairs. And then the likelihood of coincidence of dates increases significantly.
The mistake that we make in an intuitive cursory consideration of the problem is the substitution of the original problem with a similar, but not the same. The original problem is about the coincidence of birthdays for two people. And we automatically consider another problem - a specific person is selected from the group and asked what is the probability that there is another person in the group with the same date of birth. In this case, the probability of a coincidence will be much less.
Our ideas about the random are not at all random. Hearing an amazing story, how someone ended up in the right place at the right time in a completely unpredictable way, we show sincere interest, make round eyes and begin to wonder if this is fate or the hand of the Almighty?
Randomness is not a very intuitive thing. More precisely, her perception is often intuitively wrong. Everyone knows that the probability of getting heads or tails on a correct coin is ½. At the same time, nothing prevents the coin from falling heads 10 or 100 times in a row. There is no condition that heads and tails should alternate. The coin either falls heads up or it doesn't.
Incredible coincidence or pattern?
Coincidences happen a lot more often than we think. We just don't notice them. In order to notice a coincidence, it is necessary that it has specific meaning for us.
You can do a thought experiment. Imagine being introduced to a friend at a party. After that, you meet him in a bakery, in a store, then at a bus stop at the house. Maybe this person is destined for you from above and someone in heaven arranges regular meetings for you? Or you could have seen him before in the same places, just did not attach any importance to it and paid no more attention to him than to other bystanders?
You began to notice him because he became familiar to you, this particular person acquired meaning in your world.
"The paradox of birthdays"
There is a well-known paradox. Try to roughly estimate how many people should be in a group so that two people have the same date of birth (day and month) with a probability of more than 50 percent? It seems that the number of people should be large enough. But in reality, it only takes 23 people. 23 people is less than the average school class. It turns out that in a school class, it is more likely that one of the classmates will have birthdays on one day than that everyone will have their own unique birthday.
This problem is called a paradox because of the sharp discrepancy between the intuitive and mathematically correct answers.
Why is there such a difference between perception and cold math calculation? According to our estimates, the probability of being born on a certain day is quite small, and the probability that two people will be born on the same day is even less. Therefore, it turns out that our brain gives us a small probability as an answer.
What happens when you look at this from a mathematical point of view? The fact is that the problem says about the coincidence of birthdays for any two people in the group. In this case, the probability is determined by the number of pairs of people that can be made up of 23 people. From 23 people, you can make 253 unique pairs. And then the likelihood of coincidence of dates increases significantly.
The mistake that we make in an intuitive cursory consideration of the problem is the substitution of the original problem with a similar, but not the same. The original problem is about the coincidence of birthdays for two people. And we automatically consider another problem - a specific person is selected from the group and asked what is the probability that there is another person in the group with the same date of birth. In this case, the probability of a coincidence will be much less.
