Question

Неправдоподобная легенда гласит,что однажды король Франции приказал отчеканить две памятные монеты в честь великого математика Даламбера. Король захотел,чтобы при бросании этих двух монет события "Два орла" , "Две решки","Один орел и одна решка" оказались равновероятны, пусть даже монеты окажутся разной формы. Сможет ли французский монетный двор выпустить такие монеты?

Answer 1

Думаю нет,такая 100% вероятность невозможна тем более,то что шанс 2орлов сразу равен мене 25%,а чтобы сразу 6нужных тебе выпало тоже тут шанс идет практически менее 20%.
Хотя, если и шанс очень мизерный возможно получилось

Answer 2

The Legend of the French King and the Coins

The legend you mentioned states that once the King of France ordered the minting of two commemorative coins in honor of the great mathematician d'Alembert. The king wanted the events "Two Heads," "Two Tails," and "One Head and One Tail" to be equally likely when flipping these two coins, even if the coins were of different shapes. The question is whether the French mint can produce such coins.

Probability of Flipping Two Coins

To determine if it is possible to mint coins with the desired probabilities, we need to consider the probability of each event when flipping two coins. When flipping two fair coins, there are four possible outcomes: HH (two heads), HT (one head and one tail), TH (one head and one tail), and TT (two tails). Each outcome has an equal probability of 1/4 or 0.25.

Different Coin Shapes

The legend suggests that the coins may have different shapes. However, the shape of the coins does not affect the probability of the outcomes when flipping them. As long as the coins are fair, meaning they have an equal chance of landing on either side, the probabilities remain the same.

Conclusion

Based on the probabilities of flipping two coins, it is not possible to mint coins with the desired probabilities of "Two Heads," "Two Tails," and "One Head and One Tail" all being equally likely. The probability of each outcome is 0.25, and it is not possible to distribute these probabilities equally among the three events.

Therefore, the legend of the French king ordering the minting of such coins is unlikely to be true.

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