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Консультация № 160480
14.02.2009, 22:25
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Всем доброго времени суток! помогите мне пожалуйста с решением задачи по теории вероятности:
Из множества всех последовательностей, состоящих из цифр 0, 1, 2, длиной 10, случайно выбирается одна. Найти вероятность того, что выбранная последовательность содержит ровно 4 единицы.
Заранее спасибо!
Из множества всех последовательностей, состоящих из цифр 0, 1, 2, длиной 10, случайно выбирается одна. Найти вероятность того, что выбранная последовательность содержит ровно 4 единицы.
Заранее спасибо!
Обсуждение
Неизвестный
16.02.2009, 11:41
общий
22.02.2009, 00:28
это ответ
Здравствуйте, Утёмова Юлия Андреевна!
Искомая вероятность равна отношению количества 10-значных последовательностей, содержащих ровно 4 единицы, к числу всех возможных 10-значных последовательностей, составленных из 3 различных элементов.
Числитель посчитаем по формуле сочетаний (из 10 элементов по 4) по формуле C(m,n) = n!/(m!*(n-m)!)
Имеем С(4,10) = 10!/(4!*6!) = (7*8*9*10)/(1*2*3*4) = 210 !!! Правильно так: C410*A62 = 210*64 = 13440. (Сначала выбираем 4 единицы и расставляем их C410 способами; затем остальные 6 элементов заполняем нулями и двойками числом способов, равным A62.)
Знаменатель находим по формуле Размещений с повторениями
~A(m,n) = n^m
~A(10,3) = 3^10 = 59049
Тогда искомая вероятность равна210/59049 = 0.003556 (приблизительно) 13440/59049 = 0.2276...
Искомая вероятность равна отношению количества 10-значных последовательностей, содержащих ровно 4 единицы, к числу всех возможных 10-значных последовательностей, составленных из 3 различных элементов.
Числитель посчитаем по формуле сочетаний (из 10 элементов по 4) по формуле C(m,n) = n!/(m!*(n-m)!)
Имеем С(4,10) = 10!/(4!*6!) = (7*8*9*10)/(1*2*3*4) = 210 !!! Правильно так: C410*A62 = 210*64 = 13440. (Сначала выбираем 4 единицы и расставляем их C410 способами; затем остальные 6 элементов заполняем нулями и двойками числом способов, равным A62.)
Знаменатель находим по формуле Размещений с повторениями
~A(m,n) = n^m
~A(10,3) = 3^10 = 59049
Тогда искомая вероятность равна
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