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Консультация № 196956
04.11.2019, 16:03
0.00 руб.
16.11.2019, 05:50
0
1
1
Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
В игре составляются 3-буквенные слова, все буквы в которых различны и выбраны из 9 буквенного алфавита. Вероятность
того, что слово будет содержать только буквы из 6-элементного
подмножества этого 9-буквенного алфавита.
В игре составляются 3-буквенные слова, все буквы в которых различны и выбраны из 9 буквенного алфавита. Вероятность
того, что слово будет содержать только буквы из 6-элементного
подмножества этого 9-буквенного алфавита.
Обсуждение
09.11.2019, 10:56
общий
это ответ
Здравствуйте, qwerty1984mix!
Воспользуемся общей формулой: если имеется n объектов, разделённых на k групп, содержащих соответственно n[sub]1[/sub], n[sub]2[/sub],...n[sub]k[/sub] объектов (n[sub]1[/sub] + n[sub]2[/sub] + ... + n[sub]k[/sub] = n), и производится выборка m объектов (m[$8804$]n), то вероятность того, что среди них будет m[sub]1[/sub] объектов из первой группы, m[sub]2[/sub] - из второй,... m[sub]k[/sub] из k-ой группы (m[sub]1[/sub] + m[sub]2[/sub] + ... + m[sub]k[/sub] = m), равна
В данном случае n = 9 (количество букв в алфавите), k = 2, n[sub]1[/sub] = 6 (указанное в условии 6-элементное подмножество), n[sub]2[/sub] = 3 (остальные буквы), m = 3 (число букв, выбранных для слова), m[sub]1[/sub] = 3 и m[sub]2[/sub] = 0 (слово содержит 3 буквы из 6-элементного подмножества и ни одной из числа остальных). Тогда искомая вероятность будет равна:
Воспользуемся общей формулой: если имеется n объектов, разделённых на k групп, содержащих соответственно n[sub]1[/sub], n[sub]2[/sub],...n[sub]k[/sub] объектов (n[sub]1[/sub] + n[sub]2[/sub] + ... + n[sub]k[/sub] = n), и производится выборка m объектов (m[$8804$]n), то вероятность того, что среди них будет m[sub]1[/sub] объектов из первой группы, m[sub]2[/sub] - из второй,... m[sub]k[/sub] из k-ой группы (m[sub]1[/sub] + m[sub]2[/sub] + ... + m[sub]k[/sub] = m), равна
В данном случае n = 9 (количество букв в алфавите), k = 2, n[sub]1[/sub] = 6 (указанное в условии 6-элементное подмножество), n[sub]2[/sub] = 3 (остальные буквы), m = 3 (число букв, выбранных для слова), m[sub]1[/sub] = 3 и m[sub]2[/sub] = 0 (слово содержит 3 буквы из 6-элементного подмножества и ни одной из числа остальных). Тогда искомая вероятность будет равна:
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