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Консультация № 187583
23.10.2013, 16:43
79.10 руб.
0
2
2
Здравствуйте! У меня возникли сложности с таким вопросом: Из 50 экзаменационных вопросов студент подготовил 40. Определите вероятность того, что из предложенных ему четырёх вопросов, он знает по крайней мере три. Заранее благодарен.
Обсуждение
23.10.2013, 18:06
общий
это ответ
Здравствуйте, Алексей Валентинович!
Имеем количество способов выбрать четыре вопроса из 50:
количество способов ответить не менее, чем на три вопроса из четырёх:
Искомая вероятность составляет
С уважением.
Имеем количество способов выбрать четыре вопроса из 50:
количество способов ответить не менее, чем на три вопроса из четырёх:
Искомая вероятность составляет
С уважением.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
Неизвестный
23.10.2013, 19:52
общий
это ответ
Здравствуйте, Тимофеев Алексей Валентинович!
Событие состоящее в том, что он знает по крайней мере три вопроса состоит из суммы событий: А – знает 3 вопроса и В – знает 4 вопроса.
Событие А – это произведение событий (1 вопрос знает и 2 вопрос знает и 3 вопрос знает и 4 вопрос не знает).
P(3 из 4) = 40/50*39/49*38/48*10/47
Вариантов вытянуть 3 правильных вопроса из 4-х – это сочетание из 4 по 3.
Поэтому P(A) = C(4,3)*P(3 из 4)
Событие B – это произведение событий (1 вопрос знает и 2 вопрос знает и 3 вопрос знает и 4 вопрос знает).
P(4 из 4) = 40/50*39/49*38/48*37/47
Вариантов вытянуть 4 правильных вопроса из 4-х – это сочетание из 4 по 4.
Поэтому P(B) = C(4,4)*P(4 из 4)
Получаем P= P(A)+ P(B) = 0,825835866
Событие состоящее в том, что он знает по крайней мере три вопроса состоит из суммы событий: А – знает 3 вопроса и В – знает 4 вопроса.
Событие А – это произведение событий (1 вопрос знает и 2 вопрос знает и 3 вопрос знает и 4 вопрос не знает).
P(3 из 4) = 40/50*39/49*38/48*10/47
Вариантов вытянуть 3 правильных вопроса из 4-х – это сочетание из 4 по 3.
Поэтому P(A) = C(4,3)*P(3 из 4)
Событие B – это произведение событий (1 вопрос знает и 2 вопрос знает и 3 вопрос знает и 4 вопрос знает).
P(4 из 4) = 40/50*39/49*38/48*37/47
Вариантов вытянуть 4 правильных вопроса из 4-х – это сочетание из 4 по 4.
Поэтому P(B) = C(4,4)*P(4 из 4)
Получаем P= P(A)+ P(B) = 0,825835866
5
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