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Случай из покера (задачка на теорию вероятности)

Уважаемые знатоки математики, пожалуйста, поясните мне.
У меня был небольшой спор с моим знакомым. Суть в том, что мы играли в Poker Shark. На столе открыты все 5 карт. Из них 4 карты одномастные.
А у меня на руках стрит, как известно, по правилам покера, если собрать 5 одномастных карт, то это комбинация может побить стрит. Я не стал повышать ставки. Потом я выиграл, но у меня возник вопрос: а каков был шанс, что у моих соперников окажется карта той масти, 4 из которых уже на столе. Я утверждал, что шансы были очень большие, а знакомый утверждал, что шансы были низкие.
У меня на руках не было карты с нужной мастью.

Кто не знает правила.
Всего 52 карты. Получается из них 13 карт – одномастные. На столе лежит 5 карт и у меня на руках 2 (т.е. те карты, которые мы уже знаем). Получается, что остается 45 неизвестных карт, из них 9 могут иметь необходимую масть.
Со мной играет еще 4 игрока. У каждого из них на руках по 2 неизвестных карты. т.е. 8 карт.
Какова вероятность того, что из этих 8 карт хоть одна будит той же масти, что и 4 других на столе?

по моей логике:
9/45=20%, что любая карта окажется нужной, а т.к. их 8… то полюбому, одна из них может оказаться необходимой картой…

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