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Консультация № 187582
22.10.2013, 21:48
79.10 руб.
0
8
3
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос: Вероятность наличия опечатки на странице книги равна 0,0025. Какова вероятность того, что из 400 страниц опечатки имеются только на пяти страницах? Заранее благодарен.
Обсуждение
Неизвестный
22.10.2013, 22:00
общий
это ответ
Здравствуйте, Тимофеев Алексей Валентинович!
В этой задаче, по сути описывается схема Бернулли. Проводится 400 опытов (страниц), вероятность успеха (наличия опечатки) равна 0,0025. Требуется определить вероятность получения ровно 5 успехов.
Ответ на задачу равен
В этой задаче, по сути описывается схема Бернулли. Проводится 400 опытов (страниц), вероятность успеха (наличия опечатки) равна 0,0025. Требуется определить вероятность получения ровно 5 успехов.
Ответ на задачу равен
5
22.10.2013, 22:22
общий
Напишите, пожалуйста подробнее как Вы сосчитали такие большие степени. Спасибо.
22.10.2013, 22:59
общий
Адресаты:
Для аналитического решения можно воспользоваться локальной теоремой Муавра-Лапласа или формулой Пуассона, но они предоставляют грубое (приближенное) решение, поэтомув в Вашем случае лучше использовать ответ Сергея.
22.10.2013, 23:01
общий
это ответ
Здравствуйте, Тимофеев Алексей Валентинович!
В рассматриваемой ситуации схемы Бернулли, когда вероятность p мала, а число испытаний n велико, пользуются приближенной формулой распределения Пуаccона
Pn(k)=[$955$]ke-[$955$]/k!
где [$955$]=np, e - основание натуральных логарифмов.
В нашем случае p=0,0025; n=400; [$955$]=400*0,0025=1; k=5
Искомая вероятность равна
15e-1/5!=1/(120e)=0,003
В рассматриваемой ситуации схемы Бернулли, когда вероятность p мала, а число испытаний n велико, пользуются приближенной формулой распределения Пуаccона
Pn(k)=[$955$]ke-[$955$]/k!
где [$955$]=np, e - основание натуральных логарифмов.
В нашем случае p=0,0025; n=400; [$955$]=400*0,0025=1; k=5
Искомая вероятность равна
15e-1/5!=1/(120e)=0,003
5
22.10.2013, 23:04
общий
Адресаты:
они предоставляют грубое (приближенное) решение
Как видно из сравнения, результаты отличаются в 4 знаке после запятой.
Неизвестный
22.10.2013, 23:07
общий
это ответ
Здравствуйте, Тимофеев Алексей Валентинович!
Схема Бернулли.
P = C(n,k)* p**k *(1-p)**(n-k)
Она же Биномиальная функция распределения, есть в MS Excel.
p=0,0025 q = 1-p = 0,9975 n=400
k=5
P(5) = C(400,5)* 0,0025**5 *0, 9975**395 =0,003024
Схема Бернулли.
P = C(n,k)* p**k *(1-p)**(n-k)
Она же Биномиальная функция распределения, есть в MS Excel.
p=0,0025 q = 1-p = 0,9975 n=400
k=5
P(5) = C(400,5)* 0,0025**5 *0, 9975**395 =0,003024
5
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