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Консультация № 187204
14.03.2013, 15:36
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Здравствуйте! Прошу помощи в следующем вопросе:
Учебная группа состоит из 10 человек!Необходимо найти вероятность,что у нескольких из них дни рождения наступают через день(например,у первого-12 марта,у второго-13 марта,у третьего-14 марта и тд)
Учебная группа состоит из 10 человек!Необходимо найти вероятность,что у нескольких из них дни рождения наступают через день(например,у первого-12 марта,у второго-13 марта,у третьего-14 марта и тд)
Обсуждение
14.03.2013, 19:08
общий
это ответ
Здравствуйте, Ирина!
Рассмотрим матрицу "расстояний" между днями рождения: это матрица размером 10Х10, по главной диагонали которой расположены 0, а остальные элементы могут принимать целочисельные значения от -364 до 364 (729 чисел).
Нас устраивают матрицы, хотя б один элемент которых равен -1, 1, -364 или 364 ("четверка чисел").
В силу того, что матрица, состоящая из абсолютных значений этих чисел, симметрическая, рассмотрим ее половину над или под главной диагональю, то есть 45 элементов.
Количество всевозможных вариантов:
Количество вариантов, в которых никакое из 45 чисел не равно "четверке чисел" (то есть все 45 чисел могут принимать 729-4=725 разных значений):
Вероятность того, что нет "соседних" дней рождений:
Искомая вероятность равна 1-0,78=0,22.
Рассмотрим матрицу "расстояний" между днями рождения: это матрица размером 10Х10, по главной диагонали которой расположены 0, а остальные элементы могут принимать целочисельные значения от -364 до 364 (729 чисел).
Нас устраивают матрицы, хотя б один элемент которых равен -1, 1, -364 или 364 ("четверка чисел").
В силу того, что матрица, состоящая из абсолютных значений этих чисел, симметрическая, рассмотрим ее половину над или под главной диагональю, то есть 45 элементов.
Количество всевозможных вариантов:
Количество вариантов, в которых никакое из 45 чисел не равно "четверке чисел" (то есть все 45 чисел могут принимать 729-4=725 разных значений):
Вероятность того, что нет "соседних" дней рождений:
Искомая вероятность равна 1-0,78=0,22.
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