A coin throwing problem solved by von noriman

Feng nuoman, known as the "father of modern electronic computers", is also a great mathematician who once cleverly solved a coin-throwing problem.

In general, many football games or various occasions need to throw coins to make a fair choice. Because the front and back of a coin are equal probability, there is now a coin, the probability of positive and negative changes is different. How can we make a fair decision (that is, the probability of making a guess is 50% )?

Feng nuoman, the founder of "game theory", gave the following answer:This coin is discarded twice. If the two results are the same, the coin is discarded twice. If the two results are different, the first result is obtained.

Why is the probability of this 50%? We assume that the Front-up probability of the coin is 90%, and the back-up probability is 10%. Because two independent experiments, there are four situations in total:

1. Both are facing up: 81%

2. Both of them are opposite: 1%

3. The first time is positive, and the second time is negative: 9%

4. The first is the opposite, and the second is the front: 9%

If the player selects a positive orientation in the test, when the first and second cases occur, the new one will come. When the fourth and fourth cases occur, the final result will be taken, because the probability of 3, 4 is 9%, and the first results of the two types are mutually exclusive, this decision is a fair choice.

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Author: Nash _ Welcome to repost. sharing with others is the source of progress!

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